Solve 120000=1.12*81.2{left(x/1000right)}^2

$$120000 = 1.12 \cdot 81.2 { \left( \frac{ x }{ 1000 } \right) }^{ 2 }$$

Solve for x

$$x = \frac{250000 \sqrt{870}}{203} \approx 36324.830551115$$

$$x = -\frac{250000 \sqrt{870}}{203} \approx -36324.830551115$$

Steps by Finding Square Root

Multiply 1.12 and 81.2 to get 90.944.

$$120000=90.944\times \left(\frac{x}{1000}\right)^{2}$$

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

$$120000=90.944\times \frac{x^{2}}{1000^{2}}$$

Calculate 1000 to the power of 2 and get 1000000.

$$120000=90.944\times \frac{x^{2}}{1000000}$$

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

$$90.944\times \frac{x^{2}}{1000000}=120000$$

Divide both sides by 90.944.

$$\frac{x^{2}}{1000000}=\frac{120000}{90.944}$$

Expand \frac{120000}{90.944} by multiplying both numerator and the denominator by 1000.

$$\frac{x^{2}}{1000000}=\frac{120000000}{90944}$$

Reduce the fraction \frac{120000000}{90944} to lowest terms by extracting and canceling out 64.

$$\frac{x^{2}}{1000000}=\frac{1875000}{1421}$$

Multiply both sides by 1000000.

$$x^{2}=\frac{1875000}{1421}\times 1000000$$

Multiply \frac{1875000}{1421} and 1000000 to get \frac{1875000000000}{1421}.

$$x^{2}=\frac{1875000000000}{1421}$$

Take the square root of both sides of the equation.

$$x=\frac{250000\sqrt{870}}{203} x=-\frac{250000\sqrt{870}}{203}$$

Steps Using the Quadratic Formula

Multiply 1.12 and 81.2 to get 90.944.

$$120000=90.944\times \left(\frac{x}{1000}\right)^{2}$$

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

$$120000=90.944\times \frac{x^{2}}{1000^{2}}$$

Calculate 1000 to the power of 2 and get 1000000.

$$120000=90.944\times \frac{x^{2}}{1000000}$$

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

$$90.944\times \frac{x^{2}}{1000000}=120000$$

Subtract 120000 from both sides.

$$90.944\times \frac{x^{2}}{1000000}-120000=0$$

Multiply both sides of the equation by 1000000.

$$90.944x^{2}-120000000000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 90.944 for a, 0 for b, and -120000000000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 90.944\left(-120000000000\right)}}{2\times 90.944}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 90.944\left(-120000000000\right)}}{2\times 90.944}$$

Multiply -4 times 90.944.

$$x=\frac{0±\sqrt{-363.776\left(-120000000000\right)}}{2\times 90.944}$$

Multiply -363.776 times -120000000000.

$$x=\frac{0±\sqrt{43653120000000}}{2\times 90.944}$$

Take the square root of 43653120000000.

$$x=\frac{0±224000\sqrt{870}}{2\times 90.944}$$

Multiply 2 times 90.944.

$$x=\frac{0±224000\sqrt{870}}{181.888}$$

Now solve the equation x=\frac{0±224000\sqrt{870}}{181.888} when ± is plus.

$$x=\frac{250000\sqrt{870}}{203}$$

Now solve the equation x=\frac{0±224000\sqrt{870}}{181.888} when ± is minus.

$$x=-\frac{250000\sqrt{870}}{203}$$

The equation is now solved.

$$x=\frac{250000\sqrt{870}}{203} x=-\frac{250000\sqrt{870}}{203}$$