SOLUTION: (2x+1)(x+5)=-3

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Question 687953: (2x+1)(x+5)=-3
Answer by josh_jordan(263) About Me  (Show Source):
You can put this solution on YOUR website!
The first step in solving for x in this equation, is to expand the factoring on the left side of the equation:

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

2x%2Ax+%2B+2x%2A5+%2B+1x+%2B+1%2A5 =

2x%5E2+%2B+10x+%2B+1x+%2B+5 =

2x%5E2+%2B+11x+%2B+5

Next we want to set this equation equal to 0. To do this, add 3 to both sides, giving us

2x%5E2+%2B+11x+%2B+8+=+0

Now, we have a quadratic equation. Because this equation cannot be factored, we will use the quadratic formula to solve for x.

The quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

In our equation, a = 2, b = 11, and c = 8. We will plug these numbers into the quadratic formula:

%28-11+%2B-+sqrt%2811%5E2+-+4%282%29%288%29%29%29%2F%282%282%29%29 =

%28-11+%2B-+sqrt%28121+-+64%29%29%2F4 =

%28-11+%2B-+sqrt%2857%29%29%2F4

Final Answer:

x = %28-11+%2B+sqrt%2857%29%29%2F4,%28-11+-+sqrt%2857%29%29%2F4