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) * (x - 4) = 0`
Set each to 0:

`2x + 1 = 0 \\ 2x = - 1 \\ x = - (1)/(2)`

`x - 4 = 0 \\ x = 4`
Therefore, x equals 4 and -1/2