Solve x^2=3969

$$x ^ { 2 } = 3969$$

Solve for x

$$x=63$$

$$x=-63$$

Steps Using Difference of Squares

Subtract 3969 from both sides.

$$x^{2}-3969=0$$

Consider x^{2}-3969. Rewrite x^{2}-3969 as x^{2}-63^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-63\right)\left(x+63\right)=0$$

To find equation solutions, solve x-63=0 and x+63=0.

$$x=63 x=-63$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=63 x=-63$$

Steps Using the Quadratic Formula

Subtract 3969 from both sides.

$$x^{2}-3969=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -3969 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3969\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3969\right)}}{2}$$

Multiply -4 times -3969.

$$x=\frac{0±\sqrt{15876}}{2}$$

Take the square root of 15876.

$$x=\frac{0±126}{2}$$

Now solve the equation x=\frac{0±126}{2} when ± is plus. Divide 126 by 2.

$$x=63$$

Now solve the equation x=\frac{0±126}{2} when ± is minus. Divide -126 by 2.

$$x=-63$$

The equation is now solved.

$$x=63 x=-63$$