Solve x^2=50.5

$$x ^ { 2 } = 50.5$$

Solve for x

$$x = \frac{\sqrt{202}}{2} \approx 7.106335202$$

$$x = -\frac{\sqrt{202}}{2} \approx -7.106335202$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{202}}{2} x=-\frac{\sqrt{202}}{2}$$

Steps Using the Quadratic Formula

Subtract 50.5 from both sides.

$$x^{2}-50.5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -50.5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-50.5\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-50.5\right)}}{2}$$

Multiply -4 times -50.5.

$$x=\frac{0±\sqrt{202}}{2}$$

Now solve the equation x=\frac{0±\sqrt{202}}{2} when ± is plus.

$$x=\frac{\sqrt{202}}{2}$$

Now solve the equation x=\frac{0±\sqrt{202}}{2} when ± is minus.

$$x=-\frac{\sqrt{202}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{202}}{2} x=-\frac{\sqrt{202}}{2}$$