Solve 1000=5.1x^2

$$1000 = 5.1 { x }^{ 2 }$$

Solve for x

$$x = \frac{100 \sqrt{51}}{51} \approx 14.00280084$$

$$x = -\frac{100 \sqrt{51}}{51} \approx -14.00280084$$

Steps by Finding Square Root

Divide both sides by 5.1.

$$\frac{1000}{5.1}=x^{2}$$

Expand \frac{1000}{5.1} by multiplying both numerator and the denominator by 10.

$$\frac{10000}{51}=x^{2}$$

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

$$x^{2}=\frac{10000}{51}$$

Take the square root of both sides of the equation.

$$x=\frac{100\sqrt{51}}{51} x=-\frac{100\sqrt{51}}{51}$$

Steps Using the Quadratic Formula

Divide both sides by 5.1.

$$\frac{1000}{5.1}=x^{2}$$

Expand \frac{1000}{5.1} by multiplying both numerator and the denominator by 10.

$$\frac{10000}{51}=x^{2}$$

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

$$x^{2}=\frac{10000}{51}$$

Subtract \frac{10000}{51} from both sides.

$$x^{2}-\frac{10000}{51}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{10000}{51} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{10000}{51}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{10000}{51}\right)}}{2}$$

Multiply -4 times -\frac{10000}{51}.

$$x=\frac{0±\sqrt{\frac{40000}{51}}}{2}$$

Take the square root of \frac{40000}{51}.

$$x=\frac{0±\frac{200\sqrt{51}}{51}}{2}$$

Now solve the equation x=\frac{0±\frac{200\sqrt{51}}{51}}{2} when ± is plus.

$$x=\frac{100\sqrt{51}}{51}$$

Now solve the equation x=\frac{0±\frac{200\sqrt{51}}{51}}{2} when ± is minus.

$$x=-\frac{100\sqrt{51}}{51}$$

The equation is now solved.

$$x=\frac{100\sqrt{51}}{51} x=-\frac{100\sqrt{51}}{51}$$