Solve x^2-5^3=3^2

$$x ^ { 2 } - 5 ^ { 3 } = 3 ^ { 2 }$$

Solve for x

$$x=\sqrt{134}\approx 11.575836903$$

$$x=-\sqrt{134}\approx -11.575836903$$

Steps by Finding Square Root

Calculate 5 to the power of 3 and get 125.

$$x^{2}-125=3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}-125=9$$

Add 125 to both sides.

$$x^{2}=9+125$$

Add 9 and 125 to get 134.

$$x^{2}=134$$

Take the square root of both sides of the equation.

$$x=\sqrt{134} x=-\sqrt{134}$$

Steps Using the Quadratic Formula

Calculate 5 to the power of 3 and get 125.

$$x^{2}-125=3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}-125=9$$

Subtract 9 from both sides.

$$x^{2}-125-9=0$$

Subtract 9 from -125 to get -134.

$$x^{2}-134=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -134 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-134\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-134\right)}}{2}$$

Multiply -4 times -134.

$$x=\frac{0±\sqrt{536}}{2}$$

Take the square root of 536.

$$x=\frac{0±2\sqrt{134}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{134}}{2} when ± is plus.

$$x=\sqrt{134}$$

Now solve the equation x=\frac{0±2\sqrt{134}}{2} when ± is minus.

$$x=-\sqrt{134}$$

The equation is now solved.

$$x=\sqrt{134} x=-\sqrt{134}$$