Solve 6^2-(27/8)^2=x^2

$$6 ^ { 2 } - ( \frac { 27 } { 8 } ) ^ { 2 } = x ^ { 2 }$$

Solve for x

$$x = \frac{15 \sqrt{7}}{8} \approx 4.960783708$$

$$x = -\frac{15 \sqrt{7}}{8} \approx -4.960783708$$

Steps by Finding Square Root

Calculate 6 to the power of 2 and get 36.

$$36-\left(\frac{27}{8}\right)^{2}=x^{2}$$

Calculate \frac{27}{8} to the power of 2 and get \frac{729}{64}.

$$36-\frac{729}{64}=x^{2}$$

Subtract \frac{729}{64} from 36 to get \frac{1575}{64}.

$$\frac{1575}{64}=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=\frac{1575}{64}$$

Take the square root of both sides of the equation.

$$x=\frac{15\sqrt{7}}{8} x=-\frac{15\sqrt{7}}{8}$$

Steps Using the Quadratic Formula

Calculate 6 to the power of 2 and get 36.

$$36-\left(\frac{27}{8}\right)^{2}=x^{2}$$

Calculate \frac{27}{8} to the power of 2 and get \frac{729}{64}.

$$36-\frac{729}{64}=x^{2}$$

Subtract \frac{729}{64} from 36 to get \frac{1575}{64}.

$$\frac{1575}{64}=x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}=\frac{1575}{64}$$

Subtract \frac{1575}{64} from both sides.

$$x^{2}-\frac{1575}{64}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{1575}{64} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1575}{64}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{1575}{64}\right)}}{2}$$

Multiply -4 times -\frac{1575}{64}.

$$x=\frac{0±\sqrt{\frac{1575}{16}}}{2}$$

Take the square root of \frac{1575}{16}.

$$x=\frac{0±\frac{15\sqrt{7}}{4}}{2}$$

Now solve the equation x=\frac{0±\frac{15\sqrt{7}}{4}}{2} when ± is plus.

$$x=\frac{15\sqrt{7}}{8}$$

Now solve the equation x=\frac{0±\frac{15\sqrt{7}}{4}}{2} when ± is minus.

$$x=-\frac{15\sqrt{7}}{8}$$

The equation is now solved.

$$x=\frac{15\sqrt{7}}{8} x=-\frac{15\sqrt{7}}{8}$$