Solve 46.5=0.002x^2+0.01

$$46.5=0.002 { x }^{ 2 } +0.01$$

Solve for x

$$x=\sqrt{23245}\approx 152.463110292$$

$$x=-\sqrt{23245}\approx -152.463110292$$

Steps by Finding Square Root

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

$$0.002x^{2}+0.01=46.5$$

Subtract 0.01 from both sides.

$$0.002x^{2}=46.5-0.01$$

Subtract 0.01 from 46.5 to get 46.49.

$$0.002x^{2}=46.49$$

Divide both sides by 0.002.

$$x^{2}=\frac{46.49}{0.002}$$

Expand \frac{46.49}{0.002} by multiplying both numerator and the denominator by 1000.

$$x^{2}=\frac{46490}{2}$$

Divide 46490 by 2 to get 23245.

$$x^{2}=23245$$

Take the square root of both sides of the equation.

$$x=\sqrt{23245} x=-\sqrt{23245}$$

Steps Using the Quadratic Formula

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

$$0.002x^{2}+0.01=46.5$$

Subtract 46.5 from both sides.

$$0.002x^{2}+0.01-46.5=0$$

Subtract 46.5 from 0.01 to get -46.49.

$$0.002x^{2}-46.49=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 0.002 for a, 0 for b, and -46.49 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 0.002\left(-46.49\right)}}{2\times 0.002}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 0.002\left(-46.49\right)}}{2\times 0.002}$$

Multiply -4 times 0.002.

$$x=\frac{0±\sqrt{-0.008\left(-46.49\right)}}{2\times 0.002}$$

Multiply -0.008 times -46.49 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$x=\frac{0±\sqrt{0.37192}}{2\times 0.002}$$

Take the square root of 0.37192.

$$x=\frac{0±\frac{\sqrt{23245}}{250}}{2\times 0.002}$$

Multiply 2 times 0.002.

$$x=\frac{0±\frac{\sqrt{23245}}{250}}{0.004}$$

Now solve the equation x=\frac{0±\frac{\sqrt{23245}}{250}}{0.004} when ± is plus.

$$x=\sqrt{23245}$$

Now solve the equation x=\frac{0±\frac{\sqrt{23245}}{250}}{0.004} when ± is minus.

$$x=-\sqrt{23245}$$

The equation is now solved.

$$x=\sqrt{23245} x=-\sqrt{23245}$$