Solve x-7+7x-x^2

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

Factor

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

Solution Steps

Multiply and combine like terms.

$$-x^{2}+8x-7$$

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.

$$a+b=8 ab=-\left(-7\right)=7$$

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. The only such pair is the system solution.

$$a=7 b=1$$

Rewrite -x^{2}+8x-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

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

Solution Steps

Combine x and 7x to get 8x.

$$8x-7-x^{2}$$