Solve 2r(r+8)=130

$$2 r ( r + 8 ) = 130$$

Solve for r

$$r=-13$$

$$r=5$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2r by r+8.

$$2r^{2}+16r=130$$

Subtract 130 from both sides.

$$2r^{2}+16r-130=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 16 for b, and -130 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{-16±\sqrt{16^{2}-4\times 2\left(-130\right)}}{2\times 2}$$

Square 16.

$$r=\frac{-16±\sqrt{256-4\times 2\left(-130\right)}}{2\times 2}$$

Multiply -4 times 2.

$$r=\frac{-16±\sqrt{256-8\left(-130\right)}}{2\times 2}$$

Multiply -8 times -130.

$$r=\frac{-16±\sqrt{256+1040}}{2\times 2}$$

Add 256 to 1040.

$$r=\frac{-16±\sqrt{1296}}{2\times 2}$$

Take the square root of 1296.

$$r=\frac{-16±36}{2\times 2}$$

Multiply 2 times 2.

$$r=\frac{-16±36}{4}$$

Now solve the equation r=\frac{-16±36}{4} when ± is plus. Add -16 to 36.

$$r=\frac{20}{4}$$

Divide 20 by 4.

$$r=5$$

Now solve the equation r=\frac{-16±36}{4} when ± is minus. Subtract 36 from -16.

$$r=-\frac{52}{4}$$

Divide -52 by 4.

$$r=-13$$

The equation is now solved.

$$r=5 r=-13$$

Steps for Completing the Square

Use the distributive property to multiply 2r by r+8.

$$2r^{2}+16r=130$$

Divide both sides by 2.

$$\frac{2r^{2}+16r}{2}=\frac{130}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$r^{2}+\frac{16}{2}r=\frac{130}{2}$$

Divide 16 by 2.

$$r^{2}+8r=\frac{130}{2}$$

Divide 130 by 2.

$$r^{2}+8r=65$$

Divide 8, the coefficient of the x term, by 2 to get 4. Then add the square of 4 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$r^{2}+8r+4^{2}=65+4^{2}$$

Square 4.

$$r^{2}+8r+16=65+16$$

Add 65 to 16.

$$r^{2}+8r+16=81$$

Factor r^{2}+8r+16. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(r+4\right)^{2}=81$$

Take the square root of both sides of the equation.

$$\sqrt{\left(r+4\right)^{2}}=\sqrt{81}$$

Simplify.

$$r+4=9 r+4=-9$$

Subtract 4 from both sides of the equation.

$$r=5 r=-13$$