7. Solve for *x* and check. 2*x*^{2} + *x* = 21.

This is a quadratic equation, so we follow the steps for solving quadratic equations. Transpose all terms to one side leaving a 0 on the other.

2*x*^{2} + *x* - 21 = 0

Fortunately, it does factor.

(2*x* + 7)(*x* - 3) = 0

Set the factors = 0.

2*x* + 7 = 0 *x* - 3 = 0

Solve.

2*x* = -7 *x* = 3

One answer is *x* = 3. When we divide both sides of the other equaiton by 2, we get another answer of *x* = -7/2.

Check: *x* = 3:

Copy down the original equation except where you see an *x*, copy down the solutiion in parentheses.

2(3)^{2} + (3) = 21

2(9) + 3 = 21

18 + 3 = 21

and it checks. For the other answer

2(-7/2)^{2} + (-7/2) = 21

2(49/4) - 7/2 = 21

49/2 - 7/2 = 21

42/2 = 21

and they both check.