9/16x^2+7.5x=−25?

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Answer 1 · 2018-03-08T16:35:18

By moving the -25 to the left-hand side of the equation, one can factor the formula to get x, which is $-6 2/3$

$9/16x^2+7.5x+25=0$

Based on the fact that 9/16 and 25 have clean square roots (3/4 and 5, respectively) it occurred to me that the equation factored as such:

$0 =(3/4x+5)^2 = (3/4x)^2+2*5*(3/4x)+5^2$
$0 = 9/16x^2+30/4x+25$
$0 = 9/16x^2+7.5x+25$

Using the factored version, $0 = (3/4x+5)^2$ , we can now solve for x

$sqrt(0) = sqrt((3/4x+5)^2)$

$0 = 3/4x+5$

$-5 = 3/4x$

$-20/3 = x = -6 2/3$

Answer 2 · 2018-03-08T16:39:10

-20 $-:$ 3

kevin's matyh
Simply solved the equation by the formula