Solve {left(x/3right)}^2-15=7

$${ \left( \frac{ x }{ 3 } \right) }^{ 2 } -15=7$$

Solve for x

$$x=3\sqrt{22}\approx 14.071247279$$

$$x=-3\sqrt{22}\approx -14.071247279$$

Steps by Finding Square Root

To raise \frac{x}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{x^{2}}{3^{2}}-15=7$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 15 times \frac{3^{2}}{3^{2}}.

$$\frac{x^{2}}{3^{2}}-\frac{15\times 3^{2}}{3^{2}}=7$$

Since \frac{x^{2}}{3^{2}} and \frac{15\times 3^{2}}{3^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x^{2}-15\times 3^{2}}{3^{2}}=7$$

Do the multiplications in x^{2}-15\times 3^{2}.

$$\frac{x^{2}-135}{3^{2}}=7$$

Calculate 3 to the power of 2 and get 9.

$$\frac{x^{2}-135}{9}=7$$

Divide each term of x^{2}-135 by 9 to get \frac{1}{9}x^{2}-15.

$$\frac{1}{9}x^{2}-15=7$$

Add 15 to both sides.

$$\frac{1}{9}x^{2}=7+15$$

Add 7 and 15 to get 22.

$$\frac{1}{9}x^{2}=22$$

Multiply both sides by 9, the reciprocal of \frac{1}{9}.

$$x^{2}=22\times 9$$

Multiply 22 and 9 to get 198.

$$x^{2}=198$$

Take the square root of both sides of the equation.

$$x=3\sqrt{22} x=-3\sqrt{22}$$