Solve x_x^2-64=-16

$$x _ { x } ^ { 2 } - 64 = - 16$$

Solve for x_x

$$x_{x}=4\sqrt{3}\approx 6.92820323$$

$$x_{x}=-4\sqrt{3}\approx -6.92820323$$

Steps by Finding Square Root

Add 64 to both sides.

$$x_{x}^{2}=-16+64$$

Add -16 and 64 to get 48.

$$x_{x}^{2}=48$$

Take the square root of both sides of the equation.

$$x_{x}=4\sqrt{3} x_{x}=-4\sqrt{3}$$

Steps Using the Quadratic Formula

Add 16 to both sides.

$$x_{x}^{2}-64+16=0$$

Add -64 and 16 to get -48.

$$x_{x}^{2}-48=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -48 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x_{x}=\frac{0±\sqrt{0^{2}-4\left(-48\right)}}{2}$$

Square 0.

$$x_{x}=\frac{0±\sqrt{-4\left(-48\right)}}{2}$$

Multiply -4 times -48.

$$x_{x}=\frac{0±\sqrt{192}}{2}$$

Take the square root of 192.

$$x_{x}=\frac{0±8\sqrt{3}}{2}$$

Now solve the equation x_{x}=\frac{0±8\sqrt{3}}{2} when ± is plus.

$$x_{x}=4\sqrt{3}$$

Now solve the equation x_{x}=\frac{0±8\sqrt{3}}{2} when ± is minus.

$$x_{x}=-4\sqrt{3}$$

The equation is now solved.

$$x_{x}=4\sqrt{3} x_{x}=-4\sqrt{3}$$