Solve r^2-15=0

$$r ^ { 2 } - 15 = 0$$

Solve for r

$$r=\sqrt{15}\approx 3.872983346$$

$$r=-\sqrt{15}\approx -3.872983346$$

Steps by Finding Square Root

Add 15 to both sides. Anything plus zero gives itself.

$$r^{2}=15$$

Take the square root of both sides of the equation.

$$r=\sqrt{15} r=-\sqrt{15}$$

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.

$$r^{2}-15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\left(-15\right)}}{2}$$

Square 0.

$$r=\frac{0±\sqrt{-4\left(-15\right)}}{2}$$

Multiply -4 times -15.

$$r=\frac{0±\sqrt{60}}{2}$$

Take the square root of 60.

$$r=\frac{0±2\sqrt{15}}{2}$$

Now solve the equation r=\frac{0±2\sqrt{15}}{2} when ± is plus.

$$r=\sqrt{15}$$

Now solve the equation r=\frac{0±2\sqrt{15}}{2} when ± is minus.

$$r=-\sqrt{15}$$

The equation is now solved.

$$r=\sqrt{15} r=-\sqrt{15}$$