Solve 144+x^2=576

$$144+ { x }^{ 2 } = 576$$

Solve for x

$$x=12\sqrt{3}\approx 20.784609691$$

$$x=-12\sqrt{3}\approx -20.784609691$$

Steps by Finding Square Root

Subtract 144 from both sides.

$$x^{2}=576-144$$

Subtract 144 from 576 to get 432.

$$x^{2}=432$$

Take the square root of both sides of the equation.

$$x=12\sqrt{3} x=-12\sqrt{3}$$

Steps Using the Quadratic Formula

Subtract 576 from both sides.

$$144+x^{2}-576=0$$

Subtract 576 from 144 to get -432.

$$-432+x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}-432=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -432 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-432\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-432\right)}}{2}$$

Multiply -4 times -432.

$$x=\frac{0±\sqrt{1728}}{2}$$

Take the square root of 1728.

$$x=\frac{0±24\sqrt{3}}{2}$$

Now solve the equation x=\frac{0±24\sqrt{3}}{2} when ± is plus.

$$x=12\sqrt{3}$$

Now solve the equation x=\frac{0±24\sqrt{3}}{2} when ± is minus.

$$x=-12\sqrt{3}$$

The equation is now solved.

$$x=12\sqrt{3} x=-12\sqrt{3}$$