Solve x^2=42525

$${ x }^{ 2 } = 42525$$

Solve for x

$$x=45\sqrt{21}\approx 206.215906273$$

$$x=-45\sqrt{21}\approx -206.215906273$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=45\sqrt{21} x=-45\sqrt{21}$$

Steps Using the Quadratic Formula

Subtract 42525 from both sides.

$$x^{2}-42525=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -42525 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-42525\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-42525\right)}}{2}$$

Multiply -4 times -42525.

$$x=\frac{0±\sqrt{170100}}{2}$$

Take the square root of 170100.

$$x=\frac{0±90\sqrt{21}}{2}$$

Now solve the equation x=\frac{0±90\sqrt{21}}{2} when ± is plus.

$$x=45\sqrt{21}$$

Now solve the equation x=\frac{0±90\sqrt{21}}{2} when ± is minus.

$$x=-45\sqrt{21}$$

The equation is now solved.

$$x=45\sqrt{21} x=-45\sqrt{21}$$