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# Consider the equation. show work

Consider the equation 9x2 + 12x - 5=0.
(a) Find and state the value of the discriminant, b2 – 4ac. Then state whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exists. Show work.

(b) Find the exact solutions of the equation. Simplify as much as possible. Show work. You are welcome to use any of the techniques which apply and that you prefer (i.e., factoring, applying the principle of square roots, completing the square, or the quadratic formula.)

### 2 Answers by Expert Tutors

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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The procedure is

a X^2 + bx + c = 0

i.e. 9 x^2 + 12X - 5          choose 2 number is:
mn = 9(- 5) , and m +n = 12    m = 15 , n = -3 is the answer.

break 12 X = 15X -3X

9 X^2 + 15X - 3X -45 = 0

9X ( X - 5 ) - 3 ( X -5 ) =0

(9X - 3 ) ( X -5 ) =0

9X -3 =0   X = 1/3        X - 5 = 0     X = 5

Lily M. | CPA with 10+ years experience fluent in ChineseCPA with 10+ years experience fluent in ...
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(b) Factoring: 9x2+12x-5=0 => (3x+5)(3x-1)=0 => 3x+5=0 OR 3x-1=0, so x1=-5/3, x2=1/3