(2x + 5)(x+1)=-1

[Exquisite]

Can someone tell me if this is correct, and if it's not where did I go wrong?

Question: (2x + 5)(x+1)=-1

Answer:
(2x+5)(x+1)=-1
2x^2 + 2x + 5x + 5 = -1
2x^2 + 7x + 5 = -1
2x^2 + 7x = -1 + (-5)
2x^2 + 7x = -6
x (2x +7) = -6

1st X value:
x = - 6

2nd X value:

2x + 7 = -6
2x = - 6 + (-7)
2x = -13
x = -13 / 2
x = - 6 [1/2]
x = -6.5

 

[jwpaine]

\(\displaystyle \L (2x + 5)(x+1) \,=\, -1\)

\(\displaystyle \L 2x^{2}+7x+5 = -1\)

\(\displaystyle \L 2x^{2}+7x+6 = 0\)

\(\displaystyle \L 2x^2 + (4x + 3x) + 6 = 0\)

Group

\(\displaystyle \L (2x^2 + 4x) + (3x + 6) = 0\)

Factor out common terms from each binomial:

\(\displaystyle \L 2x(x + 2) + 3(x + 2) = 0\)

Factor out (x + 2) so you arrive at:

\(\displaystyle \L (x+2)(2x + 3) = 0\)

Now solve for your two roots.

John