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

all real solutions

### 3 Answers by Expert Tutors

Alex V. | College doesn't make you smart. College teaches you to be resourceful.College doesn't make you smart. College ...
4.8 4.8 (73 lesson ratings) (73)
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Once you can accomplish arranging to get ax2+bx +c = 0...

you can use the Quadratic Equation:  [-b +/- sqrt(b2 - 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
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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A general rule is:

2 X2 + 7X - 9 = 0                 to find 2 numbers whose sum is +7, and their product is -18 .
those numbers are    +9 , - 2
2X2 - 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

Students should be encouraged to factor the quadratic first. Because it is important later on, when dealing with differential equations, and solutions of higher degree equations to be able to determine the conditions in which the solutions are rational/ irrational or complex.
Richard P. | Fairfax County Tutor for HS Math and ScienceFairfax County Tutor for HS Math and Sci...
4.9 4.9 (630 lesson ratings) (630)
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This factors as

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

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