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Question 151472: I am trying to find b^2-4ac and the number of real solutions for the equation 16-24x+9x^2=0.

If I put it in standard form ax^2 + ax + a = 0
a=-9 b=24 c=-16
b^2-4ac= 24^2 - 4(-9)(-16)=576-576= 0
So: when the discriminat equals 0 there should be only one solution correct? But how do I find that 1 solution? : I am trying to find b^2-4ac and the number of real solutions for the equation 16-24x+9x^2=0.

If I put it in standard form ax^2 + ax + a = 0
a=-9 b=24 c=-16
b^2-4ac= 24^2 - 4(-9)(-16)=576-576= 0
So: when the discriminat equals 0 there should be only one solution correct? But how do I find that 1 solution?
Answer by jim_thompson5910(9421) About Me  (Show Source):
You can put this solution on YOUR website!
16-24x+9x^2=0 Start with the given equation.


9x^2-24x+16=0 Rearrange the terms.


From 9x^2-24x+16 we can see that a=9, b=-24, and c=16


D=b^2-4ac Start with the discriminant formula.


D=(-24)^2-4(9)(16) Plug in a=9, b=-24, and c=16


D=576-4(9)(16) Square -24 to get 576


D=576-576 Multiply 4(9)(16) to get (36)(16)=576


D=0 Subtract 576 from 576 to get 0


Since the discriminant is equal to zero, this means that there is one real solution.


So you are correct. However, I'm not sure where you got a=-9 b=24 c=-16 from.


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To find the one solution, you have 2 options

Option # 1 Quadratic Formula (preferred method)

9x^2-24x+16=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=16


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)(16) ))/(2(9)) Plug in a=9, b=-24, and c=16


x = (24 +- sqrt( (-24)^2-4(9)(16) ))/(2(9)) Negate -24 to get 24.


x = (24 +- sqrt( 576-4(9)(16) ))/(2(9)) Square -24 to get 576.


x = (24 +- sqrt( 576-576 ))/(2(9)) Multiply 4(9)(16) to get 576


x = (24 +- sqrt( 0 ))/(2(9)) Subtract 576 from 576 to get 0


x = (24 +- sqrt( 0 ))/(18) Multiply 2 and 9 to get 18.


x = (24 +- 0)/(18) Take the square root of 0 to get 0.


x = (24 + 0)/(18) or x = (24 - 0)/(18) Break up the expression.


x = (24)/(18) or x = (24)/(18) Combine like terms.


x = 4/3 or x = 4/3 Simplify.


So our answer is x = 4/3 (with a multiplicity of 2)



Option # 2 Factoring:

9x^2-24x+16=0 Start with the given equation

(3x-4)(3x-4)=0 Factor the left side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
3x-4=0 or 3x-4=0

x=4/3 or x=4/3 Now solve for x in each case


Since we have a repeating answer, our only answer is x=4/3