Solve x^2+76=400

$$x ^ { 2 } + 76 = 400$$

Solve for x

$$x=18$$

$$x=-18$$

Steps Using Difference of Squares

Subtract 400 from both sides.

$$x^{2}+76-400=0$$

Subtract 400 from 76 to get -324.

$$x^{2}-324=0$$

Consider x^{2}-324. Rewrite x^{2}-324 as x^{2}-18^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-18\right)\left(x+18\right)=0$$

To find equation solutions, solve x-18=0 and x+18=0.

$$x=18 x=-18$$

Steps by Finding Square Root

Subtract 76 from both sides.

$$x^{2}=400-76$$

Subtract 76 from 400 to get 324.

$$x^{2}=324$$

Take the square root of both sides of the equation.

$$x=18 x=-18$$

Steps Using the Quadratic Formula

Subtract 400 from both sides.

$$x^{2}+76-400=0$$

Subtract 400 from 76 to get -324.

$$x^{2}-324=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -324 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-324\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-324\right)}}{2}$$

Multiply -4 times -324.

$$x=\frac{0±\sqrt{1296}}{2}$$

Take the square root of 1296.

$$x=\frac{0±36}{2}$$

Now solve the equation x=\frac{0±36}{2} when ± is plus. Divide 36 by 2.

$$x=18$$

Now solve the equation x=\frac{0±36}{2} when ± is minus. Divide -36 by 2.

$$x=-18$$

The equation is now solved.

$$x=18 x=-18$$