Solve x^2-1000=0

$$x ^ { 2 } - 1000 = 0$$

Solve for x

$$x=10\sqrt{10}\approx 31.622776602$$

$$x=-10\sqrt{10}\approx -31.622776602$$

Steps by Finding Square Root

Add 1000 to both sides. Anything plus zero gives itself.

$$x^{2}=1000$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}-1000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -1000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1000\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1000\right)}}{2}$$

Multiply -4 times -1000.

$$x=\frac{0±\sqrt{4000}}{2}$$

Take the square root of 4000.

$$x=\frac{0±20\sqrt{10}}{2}$$

Now solve the equation x=\frac{0±20\sqrt{10}}{2} when ± is plus.

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

Now solve the equation x=\frac{0±20\sqrt{10}}{2} when ± is minus.

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

The equation is now solved.

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