SOLUTION: I have answered solved the equation and I believe it is right but I don't know how to check it. 9x^2+24x+15=0 (3x+5)(3x+3) (3x+5)=0 3x=-5 x= -5/3 or (3x+3)=0 3x=-3

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: I have answered solved the equation and I believe it is right but I don't know how to check it. 9x^2+24x+15=0 (3x+5)(3x+3) (3x+5)=0 3x=-5 x= -5/3 or (3x+3)=0 3x=-3       Log On


   

Question 151543: I have answered solved the equation and I believe it is right but I don't know how to check it.
9x^2+24x+15=0
(3x+5)(3x+3)
(3x+5)=0
3x=-5
x= -5/3
or
(3x+3)=0
3x=-3
x=-1
Now when I try to put it in the original equation to check it... my problem is
9(-5/3)^2+24(-5/3)+15 I don't know how to do the fractions with exponents so can you show me how to do the equation to check it? Thanks Dianne
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

9x%5E2%2B24x%2B15=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=9, b=24, and c=15


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%2824%29+%2B-+sqrt%28+%2824%29%5E2-4%289%29%2815%29+%29%29%2F%282%289%29%29 Plug in a=9, b=24, and c=15


x+=+%28-24+%2B-+sqrt%28+576-4%289%29%2815%29+%29%29%2F%282%289%29%29 Square 24 to get 576.


x+=+%28-24+%2B-+sqrt%28+576-540+%29%29%2F%282%289%29%29 Multiply 4%289%29%2815%29 to get 540


x+=+%28-24+%2B-+sqrt%28+36+%29%29%2F%282%289%29%29 Subtract 540 from 576 to get 36


x+=+%28-24+%2B-+sqrt%28+36+%29%29%2F%2818%29 Multiply 2 and 9 to get 18.


x+=+%28-24+%2B-+6%29%2F%2818%29 Take the square root of 36 to get 6.


x+=+%28-24+%2B+6%29%2F%2818%29 or x+=+%28-24+-+6%29%2F%2818%29 Break up the expression.


x+=+%28-18%29%2F%2818%29 or x+=++%28-30%29%2F%2818%29 Combine like terms.


x+=+-1 or x+=+-5%2F3 Simplify.


So our answers are x+=+-1 or x+=+-5%2F3


--------------------------------------------------

Check:

Let's check the solution x+=+-1


9x%5E2%2B24x%2B15=0 Start with the given equation.


9%28-1%29%5E2%2B24%28-1%29%2B15=0 Plug in x+=+-1


9%281%29%2B24%28-1%29%2B15=0 Square -1 to get 1


9-24%2B15=0 Multiply


0=0 Combine like terms. Since the equation is true, this means that x+=+-1 is a solution.

---------------


Let's check the solution x+=+-5%2F3


9x%5E2%2B24x%2B15=0 Start with the given equation.


9%28-5%2F3%29%5E2%2B24%28-5%2F3%29%2B15=0 Plug in x+=+-5%2F3


9%2825%2F9%29%2B24%28-5%2F3%29%2B15=0 Square -5%2F3 to get 25%2F9


25%2B24%28-5%2F3%29%2B15=0 Multiply 9 and 25%2F9 to get 9%2825%2F9%29=cross%289%29%2825%2Fcross%289%29%29=25. So in this case, the denominator is eliminated.


25-40%2B15=0 Multiply 24 and -5%2F3 to get 24%28-5%2F3%29=8%2A3%28-5%2F3%29=8%2Across%283%29%28-5%2Fcross%283%29%29=8%28-5%29=-40. So in this case, the denominator is eliminated.


0=0 Combine like terms. Since the equation is true, this means that x+=+-5%2F3 is a solution.