Solve x^2-6x+9-9-7

$$x ^ { 2 } - 6 x + 9 - 9 - 7$$

Factor

$$\left(x-7\right)\left(x+1\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{2}-6x-7$$

Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-7. To find a and b, set up a system to be solved.

$$a+b=-6 ab=1\left(-7\right)=-7$$

Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. The only such pair is the system solution.

$$a=-7 b=1$$

Rewrite x^{2}-6x-7 as \left(x^{2}-7x\right)+\left(x-7\right).

$$\left(x^{2}-7x\right)+\left(x-7\right)$$

Factor out x in x^{2}-7x.

$$x\left(x-7\right)+x-7$$

Factor out common term x-7 by using distributive property.

$$\left(x-7\right)\left(x+1\right)$$

Evaluate

$$\left(x-7\right)\left(x+1\right)$$

Solution Steps

Subtract 9 from 9 to get 0.

$$x^{2}-6x-7$$