Solve 120000=112*812{left(x/1000right)}^2

$$120000 = 112 \cdot 812 { \left( \frac{ x }{ 1000 } \right) }^{ 2 }$$

Solve for x

$$x = \frac{25000 \sqrt{87}}{203} \approx 1148.692001612$$

$$x = -\frac{25000 \sqrt{87}}{203} \approx -1148.692001612$$

Steps by Finding Square Root

Multiply 112 and 812 to get 90944.

$$120000=90944\times \left(\frac{x}{1000}\right)^{2}$$

To raise \frac{x}{1000} to a power, raise both numerator and denominator to the power and then divide.

$$120000=90944\times \frac{x^{2}}{1000^{2}}$$

Express 90944\times \frac{x^{2}}{1000^{2}} as a single fraction.

$$120000=\frac{90944x^{2}}{1000^{2}}$$

Calculate 1000 to the power of 2 and get 1000000.

$$120000=\frac{90944x^{2}}{1000000}$$

Divide 90944x^{2} by 1000000 to get \frac{1421}{15625}x^{2}.

$$120000=\frac{1421}{15625}x^{2}$$

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

$$\frac{1421}{15625}x^{2}=120000$$

Multiply both sides by \frac{15625}{1421}, the reciprocal of \frac{1421}{15625}.

$$x^{2}=120000\times \frac{15625}{1421}$$

Multiply 120000 and \frac{15625}{1421} to get \frac{1875000000}{1421}.

$$x^{2}=\frac{1875000000}{1421}$$

Take the square root of both sides of the equation.

$$x=\frac{25000\sqrt{87}}{203} x=-\frac{25000\sqrt{87}}{203}$$

Steps Using the Quadratic Formula

Multiply 112 and 812 to get 90944.

$$120000=90944\times \left(\frac{x}{1000}\right)^{2}$$

To raise \frac{x}{1000} to a power, raise both numerator and denominator to the power and then divide.

$$120000=90944\times \frac{x^{2}}{1000^{2}}$$

Express 90944\times \frac{x^{2}}{1000^{2}} as a single fraction.

$$120000=\frac{90944x^{2}}{1000^{2}}$$

Calculate 1000 to the power of 2 and get 1000000.

$$120000=\frac{90944x^{2}}{1000000}$$

Divide 90944x^{2} by 1000000 to get \frac{1421}{15625}x^{2}.

$$120000=\frac{1421}{15625}x^{2}$$

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

$$\frac{1421}{15625}x^{2}=120000$$

Subtract 120000 from both sides.

$$\frac{1421}{15625}x^{2}-120000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{1421}{15625} for a, 0 for b, and -120000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{1421}{15625}\left(-120000\right)}}{2\times \frac{1421}{15625}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{1421}{15625}\left(-120000\right)}}{2\times \frac{1421}{15625}}$$

Multiply -4 times \frac{1421}{15625}.

$$x=\frac{0±\sqrt{-\frac{5684}{15625}\left(-120000\right)}}{2\times \frac{1421}{15625}}$$

Multiply -\frac{5684}{15625} times -120000.

$$x=\frac{0±\sqrt{\frac{1091328}{25}}}{2\times \frac{1421}{15625}}$$

Take the square root of \frac{1091328}{25}.

$$x=\frac{0±\frac{112\sqrt{87}}{5}}{2\times \frac{1421}{15625}}$$

Multiply 2 times \frac{1421}{15625}.

$$x=\frac{0±\frac{112\sqrt{87}}{5}}{\frac{2842}{15625}}$$

Now solve the equation x=\frac{0±\frac{112\sqrt{87}}{5}}{\frac{2842}{15625}} when ± is plus.

$$x=\frac{25000\sqrt{87}}{203}$$

Now solve the equation x=\frac{0±\frac{112\sqrt{87}}{5}}{\frac{2842}{15625}} when ± is minus.

$$x=-\frac{25000\sqrt{87}}{203}$$

The equation is now solved.

$$x=\frac{25000\sqrt{87}}{203} x=-\frac{25000\sqrt{87}}{203}$$