Solve x^2+6x+6-22

$$x ^ { 2 } + 6 x + 6 - 22$$

Factor

$$\left(x-2\right)\left(x+8\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{2}+6x-16$$

Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-16. To find a and b, set up a system to be solved.

$$a+b=6 ab=1\left(-16\right)=-16$$

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. List all such integer pairs that give product -16.

$$-1,16 -2,8 -4,4$$

Calculate the sum for each pair.

$$-1+16=15 -2+8=6 -4+4=0$$

The solution is the pair that gives sum 6.

$$a=-2 b=8$$

Rewrite x^{2}+6x-16 as \left(x^{2}-2x\right)+\left(8x-16\right).

$$\left(x^{2}-2x\right)+\left(8x-16\right)$$

Factor out x in the first and 8 in the second group.

$$x\left(x-2\right)+8\left(x-2\right)$$

Factor out common term x-2 by using distributive property.

$$\left(x-2\right)\left(x+8\right)$$

Evaluate

$$\left(x-2\right)\left(x+8\right)$$

Solution Steps

Subtract 22 from 6 to get -16.

$$x^{2}+6x-16$$