Solve (x+3)(x+3)=64

$$( x + 3 ) ( x + 3 ) = 64$$

Solve for x

$$x=5$$

$$x=-11$$

Steps Using the Quadratic Formula

Multiply x+3 and x+3 to get \left(x+3\right)^{2}.

$$\left(x+3\right)^{2}=64$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+3\right)^{2}.

$$x^{2}+6x+9=64$$

Subtract 64 from both sides.

$$x^{2}+6x+9-64=0$$

Subtract 64 from 9 to get -55.

$$x^{2}+6x-55=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 6 for b, and -55 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-6±\sqrt{6^{2}-4\left(-55\right)}}{2}$$

Square 6.

$$x=\frac{-6±\sqrt{36-4\left(-55\right)}}{2}$$

Multiply -4 times -55.

$$x=\frac{-6±\sqrt{36+220}}{2}$$

Add 36 to 220.

$$x=\frac{-6±\sqrt{256}}{2}$$

Take the square root of 256.

$$x=\frac{-6±16}{2}$$

Now solve the equation x=\frac{-6±16}{2} when ± is plus. Add -6 to 16.

$$x=\frac{10}{2}$$

Divide 10 by 2.

$$x=5$$

Now solve the equation x=\frac{-6±16}{2} when ± is minus. Subtract 16 from -6.

$$x=-\frac{22}{2}$$

Divide -22 by 2.

$$x=-11$$

The equation is now solved.

$$x=5 x=-11$$

Steps for Completing the Square

Multiply x+3 and x+3 to get \left(x+3\right)^{2}.

$$\left(x+3\right)^{2}=64$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{64}$$

Simplify.

$$x+3=8 x+3=-8$$

Subtract 3 from both sides of the equation.

$$x=5 x=-11$$