Solve 120000=112(1102)(x/1000)^2

$$120000 = 112 ( 1102 ) ( \frac { x } { 1000 } ) ^ { 2 }$$

Solve for x

$$x = \frac{25000 \sqrt{23142}}{3857} \approx 986.031557196$$

$$x = -\frac{25000 \sqrt{23142}}{3857} \approx -986.031557196$$

Steps by Finding Square Root

Multiply 112 and 1102 to get 123424.

$$120000=123424\times \left(\frac{x}{1000}\right)^{2}$$

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

$$120000=123424\times \frac{x^{2}}{1000^{2}}$$

Express 123424\times \frac{x^{2}}{1000^{2}} as a single fraction.

$$120000=\frac{123424x^{2}}{1000^{2}}$$

Calculate 1000 to the power of 2 and get 1000000.

$$120000=\frac{123424x^{2}}{1000000}$$

Divide 123424x^{2} by 1000000 to get \frac{3857}{31250}x^{2}.

$$120000=\frac{3857}{31250}x^{2}$$

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

$$\frac{3857}{31250}x^{2}=120000$$

Multiply both sides by \frac{31250}{3857}, the reciprocal of \frac{3857}{31250}.

$$x^{2}=120000\times \frac{31250}{3857}$$

Multiply 120000 and \frac{31250}{3857} to get \frac{3750000000}{3857}.

$$x^{2}=\frac{3750000000}{3857}$$

Take the square root of both sides of the equation.

$$x=\frac{25000\sqrt{23142}}{3857} x=-\frac{25000\sqrt{23142}}{3857}$$

Steps Using the Quadratic Formula

Multiply 112 and 1102 to get 123424.

$$120000=123424\times \left(\frac{x}{1000}\right)^{2}$$

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

$$120000=123424\times \frac{x^{2}}{1000^{2}}$$

Express 123424\times \frac{x^{2}}{1000^{2}} as a single fraction.

$$120000=\frac{123424x^{2}}{1000^{2}}$$

Calculate 1000 to the power of 2 and get 1000000.

$$120000=\frac{123424x^{2}}{1000000}$$

Divide 123424x^{2} by 1000000 to get \frac{3857}{31250}x^{2}.

$$120000=\frac{3857}{31250}x^{2}$$

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

$$\frac{3857}{31250}x^{2}=120000$$

Subtract 120000 from both sides.

$$\frac{3857}{31250}x^{2}-120000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{3857}{31250} for a, 0 for b, and -120000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times \frac{3857}{31250}\left(-120000\right)}}{2\times \frac{3857}{31250}}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times \frac{3857}{31250}\left(-120000\right)}}{2\times \frac{3857}{31250}}$$

Multiply -4 times \frac{3857}{31250}.

$$x=\frac{0±\sqrt{-\frac{7714}{15625}\left(-120000\right)}}{2\times \frac{3857}{31250}}$$

Multiply -\frac{7714}{15625} times -120000.

$$x=\frac{0±\sqrt{\frac{1481088}{25}}}{2\times \frac{3857}{31250}}$$

Take the square root of \frac{1481088}{25}.

$$x=\frac{0±\frac{8\sqrt{23142}}{5}}{2\times \frac{3857}{31250}}$$

Multiply 2 times \frac{3857}{31250}.

$$x=\frac{0±\frac{8\sqrt{23142}}{5}}{\frac{3857}{15625}}$$

Now solve the equation x=\frac{0±\frac{8\sqrt{23142}}{5}}{\frac{3857}{15625}} when ± is plus.

$$x=\frac{25000\sqrt{23142}}{3857}$$

Now solve the equation x=\frac{0±\frac{8\sqrt{23142}}{5}}{\frac{3857}{15625}} when ± is minus.

$$x=-\frac{25000\sqrt{23142}}{3857}$$

The equation is now solved.

$$x=\frac{25000\sqrt{23142}}{3857} x=-\frac{25000\sqrt{23142}}{3857}$$