Solve 2*10^-7*1.98/x-1.5110^-3-2*10^-7*1.98/x+1.5110^-3=6.65{10}^-10

$$\frac{ 2 \times { 10 }^{ -7 } \times 1.98 }{ x-1.51 { 10 }^{ -3 } } - \frac{ 2 \times { 10 }^{ -7 } \times 1.98 }{ x+1.51 { 10 }^{ -3 } } = 6.65 { 10 }^{ -10 }$$

Solve for x

$$x = \frac{\sqrt{318115123326889}}{13300000} \approx 1.341036249$$

$$x = -\frac{\sqrt{318115123326889}}{13300000} \approx -1.341036249$$

Steps by Finding Square Root

Calculate 10 to the power of -7 and get \frac{1}{10000000}.

$$\frac{2\times \frac{1}{10000000}\times 1.98}{x-1.51\times 10^{-3}}-\frac{2\times 10^{-7}\times 1.98}{x+1.51\times 10^{-3}}=6.65\times 10^{-10}$$

Multiply 2 and \frac{1}{10000000} to get \frac{1}{5000000}.

$$\frac{\frac{1}{5000000}\times 1.98}{x-1.51\times 10^{-3}}-\frac{2\times 10^{-7}\times 1.98}{x+1.51\times 10^{-3}}=6.65\times 10^{-10}$$

Multiply \frac{1}{5000000} and 1.98 to get \frac{99}{250000000}.

$$\frac{\frac{99}{250000000}}{x-1.51\times 10^{-3}}-\frac{2\times 10^{-7}\times 1.98}{x+1.51\times 10^{-3}}=6.65\times 10^{-10}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{\frac{99}{250000000}}{x-1.51\times \frac{1}{1000}}-\frac{2\times 10^{-7}\times 1.98}{x+1.51\times 10^{-3}}=6.65\times 10^{-10}$$

Multiply 1.51 and \frac{1}{1000} to get \frac{151}{100000}.

$$\frac{\frac{99}{250000000}}{x-\frac{151}{100000}}-\frac{2\times 10^{-7}\times 1.98}{x+1.51\times 10^{-3}}=6.65\times 10^{-10}$$

Express \frac{\frac{99}{250000000}}{x-\frac{151}{100000}} as a single fraction.

$$\frac{99}{250000000\left(x-\frac{151}{100000}\right)}-\frac{2\times 10^{-7}\times 1.98}{x+1.51\times 10^{-3}}=6.65\times 10^{-10}$$

Calculate 10 to the power of -7 and get \frac{1}{10000000}.

$$\frac{99}{250000000\left(x-\frac{151}{100000}\right)}-\frac{2\times \frac{1}{10000000}\times 1.98}{x+1.51\times 10^{-3}}=6.65\times 10^{-10}$$

Multiply 2 and \frac{1}{10000000} to get \frac{1}{5000000}.

$$\frac{99}{250000000\left(x-\frac{151}{100000}\right)}-\frac{\frac{1}{5000000}\times 1.98}{x+1.51\times 10^{-3}}=6.65\times 10^{-10}$$

Multiply \frac{1}{5000000} and 1.98 to get \frac{99}{250000000}.

$$\frac{99}{250000000\left(x-\frac{151}{100000}\right)}-\frac{\frac{99}{250000000}}{x+1.51\times 10^{-3}}=6.65\times 10^{-10}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{99}{250000000\left(x-\frac{151}{100000}\right)}-\frac{\frac{99}{250000000}}{x+1.51\times \frac{1}{1000}}=6.65\times 10^{-10}$$

Multiply 1.51 and \frac{1}{1000} to get \frac{151}{100000}.

$$\frac{99}{250000000\left(x-\frac{151}{100000}\right)}-\frac{\frac{99}{250000000}}{x+\frac{151}{100000}}=6.65\times 10^{-10}$$

Express \frac{\frac{99}{250000000}}{x+\frac{151}{100000}} as a single fraction.

$$\frac{99}{250000000\left(x-\frac{151}{100000}\right)}-\frac{99}{250000000\left(x+\frac{151}{100000}\right)}=6.65\times 10^{-10}$$

Calculate 10 to the power of -10 and get \frac{1}{10000000000}.

$$\frac{99}{250000000\left(x-\frac{151}{100000}\right)}-\frac{99}{250000000\left(x+\frac{151}{100000}\right)}=6.65\times \frac{1}{10000000000}$$

Multiply 6.65 and \frac{1}{10000000000} to get \frac{133}{200000000000}.

$$\frac{99}{250000000\left(x-\frac{151}{100000}\right)}-\frac{99}{250000000\left(x+\frac{151}{100000}\right)}=\frac{133}{200000000000}$$

Use the distributive property to multiply 250000000 by x-\frac{151}{100000}.

$$\frac{99}{250000000x-377500}-\frac{99}{250000000\left(x+\frac{151}{100000}\right)}=\frac{133}{200000000000}$$

Use the distributive property to multiply 250000000 by x+\frac{151}{100000}.

$$\frac{99}{250000000x-377500}-\frac{99}{250000000x+377500}=\frac{133}{200000000000}$$

Factor 250000000x-377500. Factor 250000000x+377500.

$$\frac{99}{2500\left(100000x-151\right)}-\frac{99}{2500\left(100000x+151\right)}=\frac{133}{200000000000}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2500\left(100000x-151\right) and 2500\left(100000x+151\right) is 2500\left(100000x-151\right)\left(100000x+151\right). Multiply \frac{99}{2500\left(100000x-151\right)} times \frac{100000x+151}{100000x+151}. Multiply \frac{99}{2500\left(100000x+151\right)} times \frac{100000x-151}{100000x-151}.

$$\frac{99\left(100000x+151\right)}{2500\left(100000x-151\right)\left(100000x+151\right)}-\frac{99\left(100000x-151\right)}{2500\left(100000x-151\right)\left(100000x+151\right)}=\frac{133}{200000000000}$$

Since \frac{99\left(100000x+151\right)}{2500\left(100000x-151\right)\left(100000x+151\right)} and \frac{99\left(100000x-151\right)}{2500\left(100000x-151\right)\left(100000x+151\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{99\left(100000x+151\right)-99\left(100000x-151\right)}{2500\left(100000x-151\right)\left(100000x+151\right)}=\frac{133}{200000000000}$$

Do the multiplications in 99\left(100000x+151\right)-99\left(100000x-151\right).

$$\frac{9900000x+14949-9900000x+14949}{2500\left(100000x-151\right)\left(100000x+151\right)}=\frac{133}{200000000000}$$

Combine like terms in 9900000x+14949-9900000x+14949.

$$\frac{29898}{2500\left(100000x-151\right)\left(100000x+151\right)}=\frac{133}{200000000000}$$

Variable x cannot be equal to any of the values -\frac{151}{100000},\frac{151}{100000} since division by zero is not defined. Multiply both sides of the equation by 200000000000\left(100000x-151\right)\left(100000x+151\right), the least common multiple of 2500\left(100000x-151\right)\left(100000x+151\right),200000000000.

$$80000000\times 29898=133\left(100000x-151\right)\left(100000x+151\right)$$

Multiply 80000000 and 29898 to get 2391840000000.

$$2391840000000=133\left(100000x-151\right)\left(100000x+151\right)$$

Use the distributive property to multiply 133 by 100000x-151.

$$2391840000000=\left(13300000x-20083\right)\left(100000x+151\right)$$

Use the distributive property to multiply 13300000x-20083 by 100000x+151 and combine like terms.

$$2391840000000=1330000000000x^{2}-3032533$$

Swap sides so that all variable terms are on the left hand side.

$$1330000000000x^{2}-3032533=2391840000000$$

Add 3032533 to both sides.

$$1330000000000x^{2}=2391840000000+3032533$$

Add 2391840000000 and 3032533 to get 2391843032533.

$$1330000000000x^{2}=2391843032533$$

Divide both sides by 1330000000000.

$$x^{2}=\frac{2391843032533}{1330000000000}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{318115123326889}}{13300000} x=-\frac{\sqrt{318115123326889}}{13300000}$$

Steps Using the Quadratic Formula

Calculate 10 to the power of -7 and get \frac{1}{10000000}.

$$\frac{2\times \frac{1}{10000000}\times 1.98}{x-1.51\times 10^{-3}}-\frac{2\times 10^{-7}\times 1.98}{x+1.51\times 10^{-3}}=6.65\times 10^{-10}$$

Multiply 2 and \frac{1}{10000000} to get \frac{1}{5000000}.

$$\frac{\frac{1}{5000000}\times 1.98}{x-1.51\times 10^{-3}}-\frac{2\times 10^{-7}\times 1.98}{x+1.51\times 10^{-3}}=6.65\times 10^{-10}$$

Multiply \frac{1}{5000000} and 1.98 to get \frac{99}{250000000}.

$$\frac{\frac{99}{250000000}}{x-1.51\times 10^{-3}}-\frac{2\times 10^{-7}\times 1.98}{x+1.51\times 10^{-3}}=6.65\times 10^{-10}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{\frac{99}{250000000}}{x-1.51\times \frac{1}{1000}}-\frac{2\times 10^{-7}\times 1.98}{x+1.51\times 10^{-3}}=6.65\times 10^{-10}$$

Multiply 1.51 and \frac{1}{1000} to get \frac{151}{100000}.

$$\frac{\frac{99}{250000000}}{x-\frac{151}{100000}}-\frac{2\times 10^{-7}\times 1.98}{x+1.51\times 10^{-3}}=6.65\times 10^{-10}$$

Express \frac{\frac{99}{250000000}}{x-\frac{151}{100000}} as a single fraction.

$$\frac{99}{250000000\left(x-\frac{151}{100000}\right)}-\frac{2\times 10^{-7}\times 1.98}{x+1.51\times 10^{-3}}=6.65\times 10^{-10}$$

Calculate 10 to the power of -7 and get \frac{1}{10000000}.

$$\frac{99}{250000000\left(x-\frac{151}{100000}\right)}-\frac{2\times \frac{1}{10000000}\times 1.98}{x+1.51\times 10^{-3}}=6.65\times 10^{-10}$$

Multiply 2 and \frac{1}{10000000} to get \frac{1}{5000000}.

$$\frac{99}{250000000\left(x-\frac{151}{100000}\right)}-\frac{\frac{1}{5000000}\times 1.98}{x+1.51\times 10^{-3}}=6.65\times 10^{-10}$$

Multiply \frac{1}{5000000} and 1.98 to get \frac{99}{250000000}.

$$\frac{99}{250000000\left(x-\frac{151}{100000}\right)}-\frac{\frac{99}{250000000}}{x+1.51\times 10^{-3}}=6.65\times 10^{-10}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{99}{250000000\left(x-\frac{151}{100000}\right)}-\frac{\frac{99}{250000000}}{x+1.51\times \frac{1}{1000}}=6.65\times 10^{-10}$$

Multiply 1.51 and \frac{1}{1000} to get \frac{151}{100000}.

$$\frac{99}{250000000\left(x-\frac{151}{100000}\right)}-\frac{\frac{99}{250000000}}{x+\frac{151}{100000}}=6.65\times 10^{-10}$$

Express \frac{\frac{99}{250000000}}{x+\frac{151}{100000}} as a single fraction.

$$\frac{99}{250000000\left(x-\frac{151}{100000}\right)}-\frac{99}{250000000\left(x+\frac{151}{100000}\right)}=6.65\times 10^{-10}$$

Calculate 10 to the power of -10 and get \frac{1}{10000000000}.

$$\frac{99}{250000000\left(x-\frac{151}{100000}\right)}-\frac{99}{250000000\left(x+\frac{151}{100000}\right)}=6.65\times \frac{1}{10000000000}$$

Multiply 6.65 and \frac{1}{10000000000} to get \frac{133}{200000000000}.

$$\frac{99}{250000000\left(x-\frac{151}{100000}\right)}-\frac{99}{250000000\left(x+\frac{151}{100000}\right)}=\frac{133}{200000000000}$$

Use the distributive property to multiply 250000000 by x-\frac{151}{100000}.

$$\frac{99}{250000000x-377500}-\frac{99}{250000000\left(x+\frac{151}{100000}\right)}=\frac{133}{200000000000}$$

Use the distributive property to multiply 250000000 by x+\frac{151}{100000}.

$$\frac{99}{250000000x-377500}-\frac{99}{250000000x+377500}=\frac{133}{200000000000}$$

Factor 250000000x-377500. Factor 250000000x+377500.

$$\frac{99}{2500\left(100000x-151\right)}-\frac{99}{2500\left(100000x+151\right)}=\frac{133}{200000000000}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2500\left(100000x-151\right) and 2500\left(100000x+151\right) is 2500\left(100000x-151\right)\left(100000x+151\right). Multiply \frac{99}{2500\left(100000x-151\right)} times \frac{100000x+151}{100000x+151}. Multiply \frac{99}{2500\left(100000x+151\right)} times \frac{100000x-151}{100000x-151}.

$$\frac{99\left(100000x+151\right)}{2500\left(100000x-151\right)\left(100000x+151\right)}-\frac{99\left(100000x-151\right)}{2500\left(100000x-151\right)\left(100000x+151\right)}=\frac{133}{200000000000}$$

Since \frac{99\left(100000x+151\right)}{2500\left(100000x-151\right)\left(100000x+151\right)} and \frac{99\left(100000x-151\right)}{2500\left(100000x-151\right)\left(100000x+151\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{99\left(100000x+151\right)-99\left(100000x-151\right)}{2500\left(100000x-151\right)\left(100000x+151\right)}=\frac{133}{200000000000}$$

Do the multiplications in 99\left(100000x+151\right)-99\left(100000x-151\right).

$$\frac{9900000x+14949-9900000x+14949}{2500\left(100000x-151\right)\left(100000x+151\right)}=\frac{133}{200000000000}$$

Combine like terms in 9900000x+14949-9900000x+14949.

$$\frac{29898}{2500\left(100000x-151\right)\left(100000x+151\right)}=\frac{133}{200000000000}$$

Subtract \frac{133}{200000000000} from both sides.

$$\frac{29898}{2500\left(100000x-151\right)\left(100000x+151\right)}-\frac{133}{200000000000}=0$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2500\left(100000x-151\right)\left(100000x+151\right) and 200000000000 is 200000000000\left(100000x-151\right)\left(100000x+151\right). Multiply \frac{29898}{2500\left(100000x-151\right)\left(100000x+151\right)} times \frac{80000000}{80000000}. Multiply \frac{133}{200000000000} times \frac{\left(100000x-151\right)\left(100000x+151\right)}{\left(100000x-151\right)\left(100000x+151\right)}.

$$\frac{29898\times 80000000}{200000000000\left(100000x-151\right)\left(100000x+151\right)}-\frac{133\left(100000x-151\right)\left(100000x+151\right)}{200000000000\left(100000x-151\right)\left(100000x+151\right)}=0$$

Since \frac{29898\times 80000000}{200000000000\left(100000x-151\right)\left(100000x+151\right)} and \frac{133\left(100000x-151\right)\left(100000x+151\right)}{200000000000\left(100000x-151\right)\left(100000x+151\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{29898\times 80000000-133\left(100000x-151\right)\left(100000x+151\right)}{200000000000\left(100000x-151\right)\left(100000x+151\right)}=0$$

Do the multiplications in 29898\times 80000000-133\left(100000x-151\right)\left(100000x+151\right).

$$\frac{2391840000000-1330000000000x^{2}-2008300000x+2008300000x+3032533}{200000000000\left(100000x-151\right)\left(100000x+151\right)}=0$$

Combine like terms in 2391840000000-1330000000000x^{2}-2008300000x+2008300000x+3032533.

$$\frac{2391843032533-1330000000000x^{2}}{200000000000\left(100000x-151\right)\left(100000x+151\right)}=0$$

Variable x cannot be equal to any of the values -\frac{151}{100000},\frac{151}{100000} since division by zero is not defined. Multiply both sides of the equation by 200000000000\left(100000x-151\right)\left(100000x+151\right).

$$2391843032533-1330000000000x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-1330000000000x^{2}[phone]=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1330000000000 for a, 0 for b, and 2391843032533 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1330000000000\right)\times 2391843032533}}{2\left(-1330000000000\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1330000000000\right)\times 2391843032533}}{2\left(-1330000000000\right)}$$

Multiply -4 times -1330000000000.

$$x=\frac{0±\sqrt{5320000000000\times 2391843032533}}{2\left(-1330000000000\right)}$$

Multiply 5320000000000 times 2391843032533.

$$x=\frac{0±\sqrt{12724604933075560000000000}}{2\left(-1330000000000\right)}$$

Take the square root of 12724604933075560000000000.

$$x=\frac{0±200000\sqrt{318115123326889}}{2\left(-1330000000000\right)}$$

Multiply 2 times -1330000000000.

$$x=\frac{0±200000\sqrt{318115123326889}}{-2660000000000}$$

Now solve the equation x=\frac{0±200000\sqrt{318115123326889}}{-2660000000000} when ± is plus.

$$x=-\frac{\sqrt{318115123326889}}{13300000}$$

Now solve the equation x=\frac{0±200000\sqrt{318115123326889}}{-2660000000000} when ± is minus.

$$x=\frac{\sqrt{318115123326889}}{13300000}$$

The equation is now solved.

$$x=-\frac{\sqrt{318115123326889}}{13300000} x=\frac{\sqrt{318115123326889}}{13300000}$$