Solve x^2=24025

$$x ^ { 2 } = 24025$$

Solve for x

$$x=155$$

$$x=-155$$

Steps Using Difference of Squares

Subtract 24025 from both sides.

$$x^{2}-24025=0$$

Consider x^{2}-24025. Rewrite x^{2}-24025 as x^{2}-155^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-155\right)\left(x+155\right)=0$$

To find equation solutions, solve x-155=0 and x+155=0.

$$x=155 x=-155$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=155 x=-155$$

Steps Using the Quadratic Formula

Subtract 24025 from both sides.

$$x^{2}-24025=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -24025 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-24025\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-24025\right)}}{2}$$

Multiply -4 times -24025.

$$x=\frac{0±\sqrt{96100}}{2}$$

Take the square root of 96100.

$$x=\frac{0±310}{2}$$

Now solve the equation x=\frac{0±310}{2} when ± is plus. Divide 310 by 2.

$$x=155$$

Now solve the equation x=\frac{0±310}{2} when ± is minus. Divide -310 by 2.

$$x=-155$$

The equation is now solved.

$$x=155 x=-155$$