Solve 6.63*10^8*3*10^-34/3*10^-7=frac{6.63*10^-34*3*{10}^8}{540*{10}^-9}+frac{9.1*{10}^-31*{x}^2}{2}

$$\frac{ 6.63 \times { 10 }^{ 8 } \times 3 \times { 10 }^{ -34 } }{ 3 \times { 10 }^{ -7 } } = \frac{ 6.63 \times { 10 }^{ -34 } \times 3 \times { 10 }^{ 8 } }{ 540 \times { 10 }^{ -9 } } + \frac{ 9.1 \times { 10 }^{ -31 } \times { x }^{ 2 } }{ 2 }$$

Solve for x

$$x = \frac{400000 \sqrt{1785}}{21} \approx 804747.816162957$$

$$x = -\frac{400000 \sqrt{1785}}{21} \approx -804747.816162957$$

Steps by Finding Square Root

Multiply both sides of the equation by 2.

$$\frac{20000000}{3}\times 6.63\times 10^{8}\times 3\times 10^{-34}=\frac{100000000}{27}\times 6.63\times 10^{-34}\times 3\times 10^{8}+9.1\times 10^{-31}x^{2}$$

To multiply powers of the same base, add their exponents. Add 8 and -34 to get -26.

$$\frac{20000000}{3}\times 6.63\times 10^{-26}\times 3=\frac{100000000}{27}\times 6.63\times 10^{-34}\times 3\times 10^{8}+9.1\times 10^{-31}x^{2}$$

To multiply powers of the same base, add their exponents. Add -34 and 8 to get -26.

$$\frac{20000000}{3}\times 6.63\times 10^{-26}\times 3=\frac{100000000}{27}\times 6.63\times 10^{-26}\times 3+9.1\times 10^{-31}x^{2}$$

Multiply \frac{20000000}{3} and 6.63 to get 44200000.

$$44200000\times 10^{-26}\times 3=\frac{100000000}{27}\times 6.63\times 10^{-26}\times 3+9.1\times 10^{-31}x^{2}$$

Calculate 10 to the power of -26 and get \frac{1}{100000000000000000000000000}.

$$44200000\times \frac{1}{100000000000000000000000000}\times 3=\frac{100000000}{27}\times 6.63\times 10^{-26}\times 3+9.1\times 10^{-31}x^{2}$$

Multiply 44200000 and \frac{1}{100000000000000000000000000} to get \frac{221}{500000000000000000000}.

$$\frac{221}{500000000000000000000}\times 3=\frac{100000000}{27}\times 6.63\times 10^{-26}\times 3+9.1\times 10^{-31}x^{2}$$

Multiply \frac{221}{500000000000000000000} and 3 to get \frac{663}{500000000000000000000}.

$$\frac{663}{500000000000000000000}=\frac{100000000}{27}\times 6.63\times 10^{-26}\times 3+9.1\times 10^{-31}x^{2}$$

Multiply \frac{100000000}{27} and 6.63 to get \frac{221000000}{9}.

$$\frac{663}{500000000000000000000}=\frac{221000000}{9}\times 10^{-26}\times 3+9.1\times 10^{-31}x^{2}$$

Calculate 10 to the power of -26 and get \frac{1}{100000000000000000000000000}.

$$\frac{663}{500000000000000000000}=\frac{221000000}{9}\times \frac{1}{100000000000000000000000000}\times 3+9.1\times 10^{-31}x^{2}$$

Multiply \frac{221000000}{9} and \frac{1}{100000000000000000000000000} to get \frac{221}{900000000000000000000}.

$$\frac{663}{500000000000000000000}=\frac{221}{900000000000000000000}\times 3+9.1\times 10^{-31}x^{2}$$

Multiply \frac{221}{900000000000000000000} and 3 to get \frac{221}{300000000000000000000}.

$$\frac{663}{500000000000000000000}=\frac{221}{300000000000000000000}+9.1\times 10^{-31}x^{2}$$

Calculate 10 to the power of -31 and get \frac{1}{10000000000000000000000000000000}.

$$\frac{663}{500000000000000000000}=\frac{221}{300000000000000000000}+9.1\times \frac{1}{10000000000000000000000000000000}x^{2}$$

Multiply 9.1 and \frac{1}{10000000000000000000000000000000} to get \frac{91}{100000000000000000000000000000000}.

$$\frac{663}{500000000000000000000}=\frac{221}{300000000000000000000}+\frac{91}{100000000000000000000000000000000}x^{2}$$

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

$$\frac{221}{300000000000000000000}+\frac{91}{100000000000000000000000000000000}x^{2}=\frac{663}{500000000000000000000}$$

Subtract \frac{221}{300000000000000000000} from both sides.

$$\frac{91}{100000000000000000000000000000000}x^{2}=\frac{663}{500000000000000000000}-\frac{221}{300000000000000000000}$$

Subtract \frac{221}{300000000000000000000} from \frac{663}{500000000000000000000} to get \frac{221}{375000000000000000000}.

$$\frac{91}{100000000000000000000000000000000}x^{2}=\frac{221}{375000000000000000000}$$

Multiply both sides by \frac{100000000000000000000000000000000}{91}, the reciprocal of \frac{91}{100000000000000000000000000000000}.

$$x^{2}=\frac{221}{375000000000000000000}\times \frac{100000000000000000000000000000000}{91}$$

Multiply \frac{221}{375000000000000000000} and \frac{100000000000000000000000000000000}{91} to get \frac{13600000000000}{21}.

$$x^{2}=\frac{13600000000000}{21}$$

Take the square root of both sides of the equation.

$$x=\frac{400000\sqrt{1785}}{21} x=-\frac{400000\sqrt{1785}}{21}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 2.

$$\frac{20000000}{3}\times 6.63\times 10^{8}\times 3\times 10^{-34}=\frac{100000000}{27}\times 6.63\times 10^{-34}\times 3\times 10^{8}+9.1\times 10^{-31}x^{2}$$

To multiply powers of the same base, add their exponents. Add 8 and -34 to get -26.

$$\frac{20000000}{3}\times 6.63\times 10^{-26}\times 3=\frac{100000000}{27}\times 6.63\times 10^{-34}\times 3\times 10^{8}+9.1\times 10^{-31}x^{2}$$

To multiply powers of the same base, add their exponents. Add -34 and 8 to get -26.

$$\frac{20000000}{3}\times 6.63\times 10^{-26}\times 3=\frac{100000000}{27}\times 6.63\times 10^{-26}\times 3+9.1\times 10^{-31}x^{2}$$

Multiply \frac{20000000}{3} and 6.63 to get 44200000.

$$44200000\times 10^{-26}\times 3=\frac{100000000}{27}\times 6.63\times 10^{-26}\times 3+9.1\times 10^{-31}x^{2}$$

Calculate 10 to the power of -26 and get \frac{1}{100000000000000000000000000}.

$$44200000\times \frac{1}{100000000000000000000000000}\times 3=\frac{100000000}{27}\times 6.63\times 10^{-26}\times 3+9.1\times 10^{-31}x^{2}$$

Multiply 44200000 and \frac{1}{100000000000000000000000000} to get \frac{221}{500000000000000000000}.

$$\frac{221}{500000000000000000000}\times 3=\frac{100000000}{27}\times 6.63\times 10^{-26}\times 3+9.1\times 10^{-31}x^{2}$$

Multiply \frac{221}{500000000000000000000} and 3 to get \frac{663}{500000000000000000000}.

$$\frac{663}{500000000000000000000}=\frac{100000000}{27}\times 6.63\times 10^{-26}\times 3+9.1\times 10^{-31}x^{2}$$

Multiply \frac{100000000}{27} and 6.63 to get \frac{221000000}{9}.

$$\frac{663}{500000000000000000000}=\frac{221000000}{9}\times 10^{-26}\times 3+9.1\times 10^{-31}x^{2}$$

Calculate 10 to the power of -26 and get \frac{1}{100000000000000000000000000}.

$$\frac{663}{500000000000000000000}=\frac{221000000}{9}\times \frac{1}{100000000000000000000000000}\times 3+9.1\times 10^{-31}x^{2}$$

Multiply \frac{221000000}{9} and \frac{1}{100000000000000000000000000} to get \frac{221}{900000000000000000000}.

$$\frac{663}{500000000000000000000}=\frac{221}{900000000000000000000}\times 3+9.1\times 10^{-31}x^{2}$$

Multiply \frac{221}{900000000000000000000} and 3 to get \frac{221}{300000000000000000000}.

$$\frac{663}{500000000000000000000}=\frac{221}{300000000000000000000}+9.1\times 10^{-31}x^{2}$$

Calculate 10 to the power of -31 and get \frac{1}{10000000000000000000000000000000}.

$$\frac{663}{500000000000000000000}=\frac{221}{300000000000000000000}+9.1\times \frac{1}{10000000000000000000000000000000}x^{2}$$

Multiply 9.1 and \frac{1}{10000000000000000000000000000000} to get \frac{91}{100000000000000000000000000000000}.

$$\frac{663}{500000000000000000000}=\frac{221}{300000000000000000000}+\frac{91}{100000000000000000000000000000000}x^{2}$$

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

$$\frac{221}{300000000000000000000}+\frac{91}{100000000000000000000000000000000}x^{2}=\frac{663}{500000000000000000000}$$

Subtract \frac{663}{500000000000000000000} from both sides.

$$\frac{221}{300000000000000000000}+\frac{91}{100000000000000000000000000000000}x^{2}-\frac{663}{500000000000000000000}=0$$

Subtract \frac{663}{500000000000000000000} from \frac{221}{300000000000000000000} to get -\frac{221}{375000000000000000000}.

$$-\frac{221}{375000000000000000000}+\frac{91}{100000000000000000000000000000000}x^{2}=0$$

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.

$$\frac{91}{100000000000000000000000000000000}x^{2}-\frac{221}{375000000000000000000}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{91}{100000000000000000000000000000000} for a, 0 for b, and -\frac{221}{375000000000000000000} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{91}{100000000000000000000000000000000}\left(-\frac{221}{375000000000000000000}\right)}}{2\times \frac{91}{100000000000000000000000000000000}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{91}{100000000000000000000000000000000}\left(-\frac{221}{375000000000000000000}\right)}}{2\times \frac{91}{100000000000000000000000000000000}}$$

Multiply -4 times \frac{91}{100000000000000000000000000000000}.

$$x=\frac{0±\sqrt{-\frac{91}{25000000000000000000000000000000}\left(-\frac{221}{375000000000000000000}\right)}}{2\times \frac{91}{100000000000000000000000000000000}}$$

Multiply -\frac{91}{25000000000000000000000000000000} times -\frac{221}{375000000000000000000} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{\frac{20111}{9375000000000000000000000000000000000000000000000000}}}{2\times \frac{91}{100000000000000000000000000000000}}$$

Take the square root of \frac{20111}{9375000000000000000000000000000000000000000000000000}.

$$x=\frac{0±\frac{13\sqrt{1785}}{375000000000000000000000000}}{2\times \frac{91}{100000000000000000000000000000000}}$$

Multiply 2 times \frac{91}{100000000000000000000000000000000}.

$$x=\frac{0±\frac{13\sqrt{1785}}{375000000000000000000000000}}{\frac{91}{50000000000000000000000000000000}}$$

Now solve the equation x=\frac{0±\frac{13\sqrt{1785}}{375000000000000000000000000}}{\frac{91}{50000000000000000000000000000000}} when ± is plus.

$$x=\frac{400000\sqrt{1785}}{21}$$

Now solve the equation x=\frac{0±\frac{13\sqrt{1785}}{375000000000000000000000000}}{\frac{91}{50000000000000000000000000000000}} when ± is minus.

$$x=-\frac{400000\sqrt{1785}}{21}$$

The equation is now solved.

$$x=\frac{400000\sqrt{1785}}{21} x=-\frac{400000\sqrt{1785}}{21}$$