all real solutions

## 2x^2 + 7x - 9 = 0

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# 3 Answers

Once you can accomplish arranging to get ax

^{2}+bx +c = 0...you can use the Quadratic Equation: [-b +/- sqrt(b

^{2}^{ }- 4ac)] / (2a) to solve for x= [-7 +/- sqrt[49 - 4(2)(-9)] / (2(2)

= [-7 +/- sqrt[49-(-72)] / 4

= [-7 +/- sqrt(121)]/ 4

= -7/4 +/- 11/4

x = 1 and x = -9/2

A general rule is:

2 X

^{2}+ 7X - 9 = 0 to find 2 numbers whose sum is +7, and their product is -18 . those numbers are +9 , - 2

2X

^{2 }-^{ }2X^{ }+ 9X - 9 =0 break up 7X into 9X , - 2X . 2X ( X - 1) + 9 ( X - 1 ) =0 factoring by grouping .

( X - 1 ) ( 2X + 9 ) = 0

X - 1 = 0 X = 1

2X + 9 = 0 X = - 9/2

This factors as

(x-1)(2x +9) = 0

So the solutions are x = 1 and x = -9/2

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