Solve x^2=18^2-100/9

$${ x }^{ 2 } = { 18 }^{ 2 } - \frac{ 100 }{ 9 }$$

Solve for x

$$x = \frac{16 \sqrt{11}}{3} \approx 17.688665549$$

$$x = -\frac{16 \sqrt{11}}{3} \approx -17.688665549$$

Steps by Finding Square Root

Calculate 18 to the power of 2 and get 324.

$$x^{2}=324-\frac{100}{9}$$

Subtract \frac{100}{9} from 324 to get \frac{2816}{9}.

$$x^{2}=\frac{2816}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{16\sqrt{11}}{3} x=-\frac{16\sqrt{11}}{3}$$

Steps Using the Quadratic Formula

Calculate 18 to the power of 2 and get 324.

$$x^{2}=324-\frac{100}{9}$$

Subtract \frac{100}{9} from 324 to get \frac{2816}{9}.

$$x^{2}=\frac{2816}{9}$$

Subtract \frac{2816}{9} from both sides.

$$x^{2}-\frac{2816}{9}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{2816}{9} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{2816}{9}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{2816}{9}\right)}}{2}$$

Multiply -4 times -\frac{2816}{9}.

$$x=\frac{0±\sqrt{\frac{11264}{9}}}{2}$$

Take the square root of \frac{11264}{9}.

$$x=\frac{0±\frac{32\sqrt{11}}{3}}{2}$$

Now solve the equation x=\frac{0±\frac{32\sqrt{11}}{3}}{2} when ± is plus.

$$x=\frac{16\sqrt{11}}{3}$$

Now solve the equation x=\frac{0±\frac{32\sqrt{11}}{3}}{2} when ± is minus.

$$x=-\frac{16\sqrt{11}}{3}$$

The equation is now solved.

$$x=\frac{16\sqrt{11}}{3} x=-\frac{16\sqrt{11}}{3}$$