Solve x^2=35.64

$$x ^ { 2 } = 35.64$$

Solve for x

$$x = \frac{9 \sqrt{11}}{5} \approx 5.969924623$$

$$x = -\frac{9 \sqrt{11}}{5} \approx -5.969924623$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=\frac{9\sqrt{11}}{5} x=-\frac{9\sqrt{11}}{5}$$

Steps Using the Quadratic Formula

Subtract 35.64 from both sides.

$$x^{2}-35.64=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -35.64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-35.64\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-35.64\right)}}{2}$$

Multiply -4 times -35.64.

$$x=\frac{0±\sqrt{142.56}}{2}$$

Take the square root of 142.56.

$$x=\frac{0±\frac{18\sqrt{11}}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{18\sqrt{11}}{5}}{2} when ± is plus.

$$x=\frac{9\sqrt{11}}{5}$$

Now solve the equation x=\frac{0±\frac{18\sqrt{11}}{5}}{2} when ± is minus.

$$x=-\frac{9\sqrt{11}}{5}$$

The equation is now solved.

$$x=\frac{9\sqrt{11}}{5} x=-\frac{9\sqrt{11}}{5}$$