Solve r^2+6r+9=9

$$r ^ { 2 } + 6 r + 9 = 9$$

Solve for r

$$r=-6$$

$$r=0$$

Steps Using Factoring

Subtract 9 from both sides.

$$r^{2}+6r+9-9=0$$

Subtract 9 from 9 to get 0.

$$r^{2}+6r=0$$

Factor out r.

$$r\left(r+6\right)=0$$

To find equation solutions, solve r=0 and r+6=0.

$$r=0 r=-6$$

Steps Using the Quadratic Formula

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$r^{2}+6r+9=9$$

Subtract 9 from both sides of the equation.

$$r^{2}+6r+9-9=9-9$$

Subtracting 9 from itself leaves 0.

$$r^{2}+6r+9-9=0$$

Subtract 9 from 9.

$$r^{2}+6r=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 6 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{-6±\sqrt{6^{2}}}{2}$$

Take the square root of 6^{2}.

$$r=\frac{-6±6}{2}$$

Now solve the equation r=\frac{-6±6}{2} when ± is plus. Add -6 to 6.

$$r=\frac{0}{2}$$

Divide 0 by 2.

$$r=0$$

Now solve the equation r=\frac{-6±6}{2} when ± is minus. Subtract 6 from -6.

$$r=-\frac{12}{2}$$

Divide -12 by 2.

$$r=-6$$

The equation is now solved.

$$r=0 r=-6$$

Steps for Completing the Square

Factor r^{2}+6r+9. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(r+3\right)^{2}=9$$

Take the square root of both sides of the equation.

$$\sqrt{\left(r+3\right)^{2}}=\sqrt{9}$$

Simplify.

$$r+3=3 r+3=-3$$

Subtract 3 from both sides of the equation.

$$r=0 r=-6$$