Solve 1/2(.95)(x/2)^2+1/2(1.9)x^2=1.83*10^-2

$$\frac { 1 } { 2 } ( .95 ) ( \frac { x } { 2 } ) ^ { 2 } + \frac { 1 } { 2 } ( 1.9 ) x ^ { 2 } = 1.83 \cdot 10 ^ { - 2 }$$

Solve for x

$$x=\frac{\sqrt{34770}}{1425}\approx 0.130854144$$

$$x=-\frac{\sqrt{34770}}{1425}\approx -0.130854144$$

Steps by Finding Square Root

Multiply \frac{1}{2} and 0.95 to get \frac{19}{40}.

$$\frac{19}{40}\times \left(\frac{x}{2}\right)^{2}+\frac{1}{2}\times 1.9x^{2}=1.83\times 10^{-2}$$

To raise \frac{x}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{19}{40}\times \frac{x^{2}}{2^{2}}+\frac{1}{2}\times 1.9x^{2}=1.83\times 10^{-2}$$

Multiply \frac{19}{40} times \frac{x^{2}}{2^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{19x^{2}}{40\times 2^{2}}+\frac{1}{2}\times 1.9x^{2}=1.83\times 10^{-2}$$

Multiply \frac{1}{2} and 1.9 to get \frac{19}{20}.

$$\frac{19x^{2}}{40\times 2^{2}}+\frac{19}{20}x^{2}=1.83\times 10^{-2}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{19x^{2}}{40\times 2^{2}}+\frac{19}{20}x^{2}=1.83\times \frac{1}{100}$$

Multiply 1.83 and \frac{1}{100} to get \frac{183}{10000}.

$$\frac{19x^{2}}{40\times 2^{2}}+\frac{19}{20}x^{2}=\frac{183}{10000}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{19x^{2}}{40\times 4}+\frac{19}{20}x^{2}=\frac{183}{10000}$$

Multiply 40 and 4 to get 160.

$$\frac{19x^{2}}{160}+\frac{19}{20}x^{2}=\frac{183}{10000}$$

Multiply both sides of the equation by 20000, the least common multiple of 160,20,10000.

$$125\times 19x^{2}+19000x^{2}=366$$

Reorder the terms.

$$19\times 125x^{2}+19000x^{2}=366$$

Multiply 19 and 125 to get 2375.

$$2375x^{2}+19000x^{2}=366$$

Combine 2375x^{2} and 19000x^{2} to get 21375x^{2}.

$$21375x^{2}=366$$

Divide both sides by 21375.

$$x^{2}=\frac{366}{21375}$$

Reduce the fraction \frac{366}{21375} to lowest terms by extracting and canceling out 3.

$$x^{2}=\frac{122}{7125}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{34770}}{1425} x=-\frac{\sqrt{34770}}{1425}$$

Steps Using the Quadratic Formula

Multiply \frac{1}{2} and 0.95 to get \frac{19}{40}.

$$\frac{19}{40}\times \left(\frac{x}{2}\right)^{2}+\frac{1}{2}\times 1.9x^{2}=1.83\times 10^{-2}$$

To raise \frac{x}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{19}{40}\times \frac{x^{2}}{2^{2}}+\frac{1}{2}\times 1.9x^{2}=1.83\times 10^{-2}$$

Multiply \frac{19}{40} times \frac{x^{2}}{2^{2}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{19x^{2}}{40\times 2^{2}}+\frac{1}{2}\times 1.9x^{2}=1.83\times 10^{-2}$$

Multiply \frac{1}{2} and 1.9 to get \frac{19}{20}.

$$\frac{19x^{2}}{40\times 2^{2}}+\frac{19}{20}x^{2}=1.83\times 10^{-2}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{19x^{2}}{40\times 2^{2}}+\frac{19}{20}x^{2}=1.83\times \frac{1}{100}$$

Multiply 1.83 and \frac{1}{100} to get \frac{183}{10000}.

$$\frac{19x^{2}}{40\times 2^{2}}+\frac{19}{20}x^{2}=\frac{183}{10000}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{19x^{2}}{40\times 4}+\frac{19}{20}x^{2}=\frac{183}{10000}$$

Multiply 40 and 4 to get 160.

$$\frac{19x^{2}}{160}+\frac{19}{20}x^{2}=\frac{183}{10000}$$

Subtract \frac{183}{10000} from both sides.

$$\frac{19x^{2}}{160}+\frac{19}{20}x^{2}-\frac{183}{10000}=0$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 160 and 10000 is 20000. Multiply \frac{19x^{2}}{160} times \frac{125}{125}. Multiply \frac{183}{10000} times \frac{2}{2}.

$$\frac{125\times 19x^{2}}{20000}+\frac{19}{20}x^{2}-\frac{183\times 2}{20000}=0$$

Since \frac{125\times 19x^{2}}{20000} and \frac{183\times 2}{20000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{125\times 19x^{2}-183\times 2}{20000}+\frac{19}{20}x^{2}=0$$

Do the multiplications in 125\times 19x^{2}-183\times 2.

$$\frac{2375x^{2}-366}{20000}+\frac{19}{20}x^{2}=0$$

Multiply both sides of the equation by 20000, the least common multiple of 20000,20.

$$2375x^{2}-366+19000x^{2}=0$$

Reorder the terms.

$$2375x^{2}+19000x^{2}-366=0$$

Combine 2375x^{2} and 19000x^{2} to get 21375x^{2}.

$$21375x^{2}-366=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 21375 for a, 0 for b, and -366 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 21375\left(-366\right)}}{2\times 21375}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 21375\left(-366\right)}}{2\times 21375}$$

Multiply -4 times 21375.

$$x=\frac{0±\sqrt{-85500\left(-366\right)}}{2\times 21375}$$

Multiply -85500 times -366.

$$x=\frac{0±\sqrt{31293000}}{2\times 21375}$$

Take the square root of 31293000.

$$x=\frac{0±30\sqrt{34770}}{2\times 21375}$$

Multiply 2 times 21375.

$$x=\frac{0±30\sqrt{34770}}{42750}$$

Now solve the equation x=\frac{0±30\sqrt{34770}}{42750} when ± is plus.

$$x=\frac{\sqrt{34770}}{1425}$$

Now solve the equation x=\frac{0±30\sqrt{34770}}{42750} when ± is minus.

$$x=-\frac{\sqrt{34770}}{1425}$$

The equation is now solved.

$$x=\frac{\sqrt{34770}}{1425} x=-\frac{\sqrt{34770}}{1425}$$