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

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

Factor

$$\left(2x-7\right)\left(x+7\right)$$

Solution Steps

Multiply and combine like terms.

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

Factor the expression by grouping. First, the expression needs to be rewritten as 2x^{2}+ax+bx-49. To find a and b, set up a system to be solved.

$$a+b=7 ab=2\left(-49\right)=-98$$

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 -98.

$$-1,98 -2,49 -7,14$$

Calculate the sum for each pair.

$$-1+98=97 -2+49=47 -7+14=7$$

The solution is the pair that gives sum 7.

$$a=-7 b=14$$

Rewrite 2x^{2}+7x-49 as \left(2x^{2}-7x\right)+\left(14x-49\right).

$$\left(2x^{2}-7x\right)+\left(14x-49\right)$$

Factor out x in the first and 7 in the second group.

$$x\left(2x-7\right)+7\left(2x-7\right)$$

Factor out common term 2x-7 by using distributive property.

$$\left(2x-7\right)\left(x+7\right)$$

Evaluate

$$\left(2x-7\right)\left(x+7\right)$$

Solution Steps

Combine x^{2} and x^{2} to get 2x^{2}.

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