Solve x^2=361

$${ x }^{ 2 } =361$$

Solve for x

$$x=19$$

$$x=-19$$

Steps Using Difference of Squares

Subtract 361 from both sides.

$$x^{2}-361=0$$

Consider x^{2}-361. Rewrite x^{2}-361 as x^{2}-19^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-19\right)\left(x+19\right)=0$$

To find equation solutions, solve x-19=0 and x+19=0.

$$x=19 x=-19$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=19 x=-19$$

Steps Using the Quadratic Formula

Subtract 361 from both sides.

$$x^{2}-361=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -361 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-361\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-361\right)}}{2}$$

Multiply -4 times -361.

$$x=\frac{0±\sqrt{1444}}{2}$$

Take the square root of 1444.

$$x=\frac{0±38}{2}$$

Now solve the equation x=\frac{0±38}{2} when ± is plus. Divide 38 by 2.

$$x=19$$

Now solve the equation x=\frac{0±38}{2} when ± is minus. Divide -38 by 2.

$$x=-19$$

The equation is now solved.

$$x=19 x=-19$$