Question

Are each of the following solutions of 4x^2-10x-2=2(2x+3) A.-4 B.-1/2 C.2 D.4

Answer 1

$4 {x}^{2} - 10x - 2 = 2(2x + 3)$
Factor in the 2:
$4 {x}^{2} - 10x - 2 = 4x + 6$
Subtract the right side of the = from the left:

$4 {x}^{2} - 14x - 8 = 0$
Divide both sides by 2:
$2 {x}^{2} - 7x - 4 = 0$
Split:
$(2x + 1) \times (x - 4) = 0$
Set each to 0:
$2x + 1 = 0 \\ 2x = - 1 \\ x = - \frac{1}{2}$
$x - 4 = 0 \\ x = 4$
Therefore, x equals 4 and -1/2