SOLUTION: find the real solution to the equation 9x^2=30x-25 let u=x^2 i substitute u for x^2 so I get 9u but then do I make 30x square root of 30x and move it and 25 to the other si

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: find the real solution to the equation 9x^2=30x-25 let u=x^2 i substitute u for x^2 so I get 9u but then do I make 30x square root of 30x and move it and 25 to the other si      Log On


   

Question 162320: find the real solution to the equation 9x^2=30x-25 let u=x^2
i substitute u for x^2 so I get 9u but then do I make 30x square root of 30x and move it and 25 to the other side of the equation after that? or use the power principle? confused thank you
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
find the real solution to the equation 9x^2=30x-25 let u=x^2
i substitute u for x^2 so I get 9u but then do I make 30x square root of 30x and move it and 25 to the other side of the equation after that? or use the power principle? confused thank you
-----------------------
That substitution won't help. Use the quadratic solution.
9x^2=30x-25
9x^2 - 30x + 25 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 9x%5E2%2B-30x%2B25+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-30%29%5E2-4%2A9%2A25=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%28-30%29%29%2F2%5C9.
Expression can be factored: 9x%5E2%2B-30x%2B25+=+%28x-1.66666666666667%29%2A%28x-1.66666666666667%29

Again, the answer is: 1.66666666666667, 1.66666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B-30%2Ax%2B25+%29


Or, take the sqrt of both sides:
9x^2 - 30x + 25 = 0
(3x-5)^2 = 0
3x-5 = 0
x = 5/3 Only one answer, since +0 and -0 are the same.
email me with any questions about this.