Solve r^2-24=0

$$r ^ { 2 } - 24 = 0$$

Solve for r

$$r=2\sqrt{6}\approx 4.898979486$$

$$r=-2\sqrt{6}\approx -4.898979486$$

Steps by Finding Square Root

Add 24 to both sides. Anything plus zero gives itself.

$$r^{2}=24$$

Take the square root of both sides of the equation.

$$r=2\sqrt{6} r=-2\sqrt{6}$$

Steps Using the Quadratic Formula

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.

$$r^{2}-24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\left(-24\right)}}{2}$$

Square 0.

$$r=\frac{0±\sqrt{-4\left(-24\right)}}{2}$$

Multiply -4 times -24.

$$r=\frac{0±\sqrt{96}}{2}$$

Take the square root of 96.

$$r=\frac{0±4\sqrt{6}}{2}$$

Now solve the equation r=\frac{0±4\sqrt{6}}{2} when ± is plus.

$$r=2\sqrt{6}$$

Now solve the equation r=\frac{0±4\sqrt{6}}{2} when ± is minus.

$$r=-2\sqrt{6}$$

The equation is now solved.

$$r=2\sqrt{6} r=-2\sqrt{6}$$