Solve x^2-400=0

$$x ^ { 2 } - 400 = 0$$

Solve for x

$$x=20$$

$$x=-20$$

Steps Using Difference of Squares

Consider x^{2}-400. Rewrite x^{2}-400 as x^{2}-20^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-20\right)\left(x+20\right)=0$$

To find equation solutions, solve x-20=0 and x+20=0.

$$x=20 x=-20$$

Steps by Finding Square Root

Add 400 to both sides. Anything plus zero gives itself.

$$x^{2}=400$$

Take the square root of both sides of the equation.

$$x=20 x=-20$$

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.

$$x^{2}-400=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -400 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-400\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-400\right)}}{2}$$

Multiply -4 times -400.

$$x=\frac{0±\sqrt{1600}}{2}$$

Take the square root of 1600.

$$x=\frac{0±40}{2}$$

Now solve the equation x=\frac{0±40}{2} when ± is plus. Divide 40 by 2.

$$x=20$$

Now solve the equation x=\frac{0±40}{2} when ± is minus. Divide -40 by 2.

$$x=-20$$

The equation is now solved.

$$x=20 x=-20$$