Solve (x^2+11x+30)+(x+6)

$$( x ^ { 2 } + 11 x + 30 ) + ( x + 6 )$$

Evaluate

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

Solution Steps

Combine 11x and x to get 12x.

$$x^{2}+12x+30+6$$

Add 30 and 6 to get 36.

$$x^{2}+12x+36$$

Factor

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

Solution Steps

Multiply and combine like terms.

$$x^{2}+12x+36$$

Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx+36. To find a and b, set up a system to be solved.

$$a+b=12 ab=1\times 36=36$$

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 36.

$$1,36 2,18 3,12 4,9 6,6$$

Calculate the sum for each pair.

$$1+36=37 2+18=20 3+12=15 4+9=13 6+6=12$$

The solution is the pair that gives sum 12.

$$a=6 b=6$$

Rewrite x^{2}+12x+36 as \left(x^{2}+6x\right)+\left(6x+36\right).

$$\left(x^{2}+6x\right)+\left(6x+36\right)$$

Factor out x in the first and 6 in the second group.

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

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

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

Rewrite as a binomial square.

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