Solve 7x-35-x^2+5x

$$7 x - 35 - x ^ { 2 } + 5 x$$

Factor

$$\left(5-x\right)\left(x-7\right)$$

Solution Steps

Multiply and combine like terms.

$$-x^{2}+12x-35$$

Factor the expression by grouping. First, the expression needs to be rewritten as -x^{2}+ax+bx-35. To find a and b, set up a system to be solved.

$$a+b=12 ab=-\left(-35\right)=35$$

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 35.

$$1,35 5,7$$

Calculate the sum for each pair.

$$1+35=36 5+7=12$$

The solution is the pair that gives sum 12.

$$a=7 b=5$$

Rewrite -x^{2}+12x-35 as \left(-x^{2}+7x\right)+\left(5x-35\right).

$$\left(-x^{2}+7x\right)+\left(5x-35\right)$$

Factor out -x in the first and 5 in the second group.

$$-x\left(x-7\right)+5\left(x-7\right)$$

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

$$\left(x-7\right)\left(-x+5\right)$$

Evaluate

$$\left(5-x\right)\left(x-7\right)$$

Solution Steps

Combine 7x and 5x to get 12x.

$$12x-35-x^{2}$$