Solve 22x^2=100

$$22 x ^ { 2 } = 100$$

Solve for x

$$x = \frac{5 \sqrt{22}}{11} \approx 2.132007164$$

$$x = -\frac{5 \sqrt{22}}{11} \approx -2.132007164$$

Steps by Finding Square Root

Divide both sides by 22.

$$x^{2}=\frac{100}{22}$$

Reduce the fraction \frac{100}{22} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{50}{11}$$

Take the square root of both sides of the equation.

$$x=\frac{5\sqrt{22}}{11} x=-\frac{5\sqrt{22}}{11}$$

Steps Using the Quadratic Formula

Divide both sides by 22.

$$x^{2}=\frac{100}{22}$$

Reduce the fraction \frac{100}{22} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{50}{11}$$

Subtract \frac{50}{11} from both sides.

$$x^{2}-\frac{50}{11}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{50}{11} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{50}{11}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{50}{11}\right)}}{2}$$

Multiply -4 times -\frac{50}{11}.

$$x=\frac{0±\sqrt{\frac{200}{11}}}{2}$$

Take the square root of \frac{200}{11}.

$$x=\frac{0±\frac{10\sqrt{22}}{11}}{2}$$

Now solve the equation x=\frac{0±\frac{10\sqrt{22}}{11}}{2} when ± is plus.

$$x=\frac{5\sqrt{22}}{11}$$

Now solve the equation x=\frac{0±\frac{10\sqrt{22}}{11}}{2} when ± is minus.

$$x=-\frac{5\sqrt{22}}{11}$$

The equation is now solved.

$$x=\frac{5\sqrt{22}}{11} x=-\frac{5\sqrt{22}}{11}$$