Solve x^2-63=378

$$x ^ { 2 } - 63 = 378$$

Solve for x

$$x=21$$

$$x=-21$$

Steps Using Difference of Squares

Subtract 378 from both sides.

$$x^{2}-63-378=0$$

Subtract 378 from -63 to get -441.

$$x^{2}-441=0$$

Consider x^{2}-441. Rewrite x^{2}-441 as x^{2}-21^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-21\right)\left(x+21\right)=0$$

To find equation solutions, solve x-21=0 and x+21=0.

$$x=21 x=-21$$

Steps by Finding Square Root

Add 63 to both sides.

$$x^{2}=378+63$$

Add 378 and 63 to get 441.

$$x^{2}=441$$

Take the square root of both sides of the equation.

$$x=21 x=-21$$

Steps Using the Quadratic Formula

Subtract 378 from both sides.

$$x^{2}-63-378=0$$

Subtract 378 from -63 to get -441.

$$x^{2}-441=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -441 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-441\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-441\right)}}{2}$$

Multiply -4 times -441.

$$x=\frac{0±\sqrt{1764}}{2}$$

Take the square root of 1764.

$$x=\frac{0±42}{2}$$

Now solve the equation x=\frac{0±42}{2} when ± is plus. Divide 42 by 2.

$$x=21$$

Now solve the equation x=\frac{0±42}{2} when ± is minus. Divide -42 by 2.

$$x=-21$$

The equation is now solved.

$$x=21 x=-21$$