SOLUTION: Solve for x. 4x^2=-13x-10

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Question 573163: Solve for x. 4x^2=-13x-10
Answer by mathsmiles(68) About Me  (Show Source):
You can put this solution on YOUR website!
4x^2 = -13x - 10

Let's move things around to get this into standard form:
4x^2 + 13x + 10 = 0

Now we have two possibilities:
(4X + _)(X + _) or (2x + _)(2x + _)
Need to try a few to see. At least I don't know any quick and easy method for doing this with non-1 x^2 factor.

(4X + 5)(X + 2) = Foil: 4X^2 + 8X + 5X + 10 = 4X^2 + 13X + 10. Pure luck!!

Solving using these factors:
(4X+5)(X+2) = 0
(4X + 5) = 0
4X = -5
X = -5/4
AND
(x+2) = 0
x = -2

Checking:
4(-5/4)^2 = -13(-5/4) - 10
4(25/16) = 65/4 - 10 Factoring the 4 from the first term gives ..
25/4 = 65/4 - 40/4
25/4 = 25/4 Correct!

4(-2)^2 = -13(-2) - 10
4 (4) = 26 - 10
16 = 16 Correct!