7. Solve for   x   and check. 2x2 + 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.

2x2 + x - 21 = 0

Fortunately, it does factor.

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

Set the factors = 0.

2x + 7 = 0     x - 3 = 0

Solve.

2x = -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.