Questions on Algebra: Quadratic Equation answered by real tutors!

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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: 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(9421) About Me  (Show Source):
You can put this solution on YOUR website!

9x^2+24x+15=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax^2+bx+c where a=9, b=24, and c=15


Let's use the quadratic formula to solve for x


x = (-b +- sqrt( b^2-4ac ))/(2a) Start with the quadratic formula


x = (-(24) +- sqrt( (24)^2-4(9)(15) ))/(2(9)) Plug in a=9, b=24, and c=15


x = (-24 +- sqrt( 576-4(9)(15) ))/(2(9)) Square 24 to get 576.


x = (-24 +- sqrt( 576-540 ))/(2(9)) Multiply 4(9)(15) to get 540


x = (-24 +- sqrt( 36 ))/(2(9)) Subtract 540 from 576 to get 36


x = (-24 +- sqrt( 36 ))/(18) Multiply 2 and 9 to get 18.


x = (-24 +- 6)/(18) Take the square root of 36 to get 6.


x = (-24 + 6)/(18) or x = (-24 - 6)/(18) Break up the expression.


x = (-18)/(18) or x = (-30)/(18) Combine like terms.


x = -1 or x = -5/3 Simplify.


So our answers are x = -1 or x = -5/3


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Check:

Let's check the solution x = -1


9x^2+24x+15=0 Start with the given equation.


9(-1)^2+24(-1)+15=0 Plug in x = -1


9(1)+24(-1)+15=0 Square -1 to get 1


9-24+15=0 Multiply


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

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Let's check the solution x = -5/3


9x^2+24x+15=0 Start with the given equation.


9(-5/3)^2+24(-5/3)+15=0 Plug in x = -5/3


9(25/9)+24(-5/3)+15=0 Square -5/3 to get 25/9


25+24(-5/3)+15=0 Multiply 9 and 25/9 to get 9(25/9)=cross(9)(25/cross(9))=25. So in this case, the denominator is eliminated.


25-40+15=0 Multiply 24 and -5/3 to get 24(-5/3)=8*3(-5/3)=8*cross(3)(-5/cross(3))=8(-5)=-40. So in this case, the denominator is eliminated.


0=0 Combine like terms. Since the equation is true, this means that x = -5/3 is a solution.