Solve 2x^2=1000

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

Solve for x

$$x=10\sqrt{5}\approx 22.360679775$$

$$x=-10\sqrt{5}\approx -22.360679775$$

Steps by Finding Square Root

Divide both sides by 2.

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

Divide 1000 by 2 to get 500.

$$x^{2}=500$$

Take the square root of both sides of the equation.

$$x=10\sqrt{5} x=-10\sqrt{5}$$

Steps Using the Quadratic Formula

Divide both sides by 2.

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

Divide 1000 by 2 to get 500.

$$x^{2}=500$$

Subtract 500 from both sides.

$$x^{2}-500=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -500 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-500\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-500\right)}}{2}$$

Multiply -4 times -500.

$$x=\frac{0±\sqrt{2000}}{2}$$

Take the square root of 2000.

$$x=\frac{0±20\sqrt{5}}{2}$$

Now solve the equation x=\frac{0±20\sqrt{5}}{2} when ± is plus.

$$x=10\sqrt{5}$$

Now solve the equation x=\frac{0±20\sqrt{5}}{2} when ± is minus.

$$x=-10\sqrt{5}$$

The equation is now solved.

$$x=10\sqrt{5} x=-10\sqrt{5}$$