Solve (x^2-49)+(x-7)

$$( x ^ { 2 } - 49 ) + ( x - 7 )$$

Factor

$$\left(x-7\right)\left(x+8\right)$$

Solution Steps

Multiply and combine like terms.

$$x^{2}+x-56$$

Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-56. To find a and b, set up a system to be solved.

$$a+b=1 ab=1\left(-56\right)=-56$$

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 -56.

$$-1,56 -2,28 -4,14 -7,8$$

Calculate the sum for each pair.

$$-1+56=55 -2+28=26 -4+14=10 -7+8=1$$

The solution is the pair that gives sum 1.

$$a=-7 b=8$$

Rewrite x^{2}+x-56 as \left(x^{2}-7x\right)+\left(8x-56\right).

$$\left(x^{2}-7x\right)+\left(8x-56\right)$$

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

$$x\left(x-7\right)+8\left(x-7\right)$$

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

$$\left(x-7\right)\left(x+8\right)$$

Evaluate

$$\left(x-7\right)\left(x+8\right)$$

Solution Steps

Subtract 7 from -49 to get -56.

$$x^{2}-56+x$$