Solve (x+8)^2=4

$$( x + 8 ) ^ { 2 } = 4$$

Solve for x

$$x=-6$$

$$x=-10$$

Steps Using Factoring

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+8\right)^{2}.

$$x^{2}+16x+64=4$$

Subtract 4 from both sides.

$$x^{2}+16x+64-4=0$$

Subtract 4 from 64 to get 60.

$$x^{2}+16x+60=0$$

To solve the equation, factor x^{2}+16x+60 using formula x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right). To find a and b, set up a system to be solved.

$$a+b=16 ab=60$$

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 60.

$$1,60 2,30 3,20 4,15 5,12 6,10$$

Calculate the sum for each pair.

$$1+60=61 2+30=32 3+20=23 4+15=19 5+12=17 6+10=16$$

The solution is the pair that gives sum 16.

$$a=6 b=10$$

Rewrite factored expression \left(x+a\right)\left(x+b\right) using the obtained values.

$$\left(x+6\right)\left(x+10\right)$$

To find equation solutions, solve x+6=0 and x+10=0.

$$x=-6 x=-10$$

Steps Using Factoring By Grouping

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+8\right)^{2}.

$$x^{2}+16x+64=4$$

Subtract 4 from both sides.

$$x^{2}+16x+64-4=0$$

Subtract 4 from 64 to get 60.

$$x^{2}+16x+60=0$$

To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as x^{2}+ax+bx+60. To find a and b, set up a system to be solved.

$$a+b=16 ab=1\times 60=60$$

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 60.

$$1,60 2,30 3,20 4,15 5,12 6,10$$

Calculate the sum for each pair.

$$1+60=61 2+30=32 3+20=23 4+15=19 5+12=17 6+10=16$$

The solution is the pair that gives sum 16.

$$a=6 b=10$$

Rewrite x^{2}+16x+60 as \left(x^{2}+6x\right)+\left(10x+60\right).

$$\left(x^{2}+6x\right)+\left(10x+60\right)$$

Factor out x in the first and 10 in the second group.

$$x\left(x+6\right)+10\left(x+6\right)$$

Factor out common term x+6 by using distributive property.

$$\left(x+6\right)\left(x+10\right)$$

To find equation solutions, solve x+6=0 and x+10=0.

$$x=-6 x=-10$$

Steps Using the Quadratic Formula

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+8\right)^{2}.

$$x^{2}+16x+64=4$$

Subtract 4 from both sides.

$$x^{2}+16x+64-4=0$$

Subtract 4 from 64 to get 60.

$$x^{2}+16x+60=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 16 for b, and 60 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-16±\sqrt{16^{2}-4\times 60}}{2}$$

Square 16.

$$x=\frac{-16±\sqrt{256-4\times 60}}{2}$$

Multiply -4 times 60.

$$x=\frac{-16±\sqrt{256-240}}{2}$$

Add 256 to -240.

$$x=\frac{-16±\sqrt{16}}{2}$$

Take the square root of 16.

$$x=\frac{-16±4}{2}$$

Now solve the equation x=\frac{-16±4}{2} when ± is plus. Add -16 to 4.

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

Divide -12 by 2.

$$x=-6$$

Now solve the equation x=\frac{-16±4}{2} when ± is minus. Subtract 4 from -16.

$$x=-\frac{20}{2}$$

Divide -20 by 2.

$$x=-10$$

The equation is now solved.

$$x=-6 x=-10$$

Steps for Completing the Square

Take the square root of both sides of the equation.

$$\sqrt{\left(x+8\right)^{2}}=\sqrt{4}$$

Simplify.

$$x+8=2 x+8=-2$$

Subtract 8 from both sides of the equation.

$$x=-6 x=-10$$