SOLUTION: 4x^2-15x+9=0

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Question 273826: 4x^2-15x+9=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
For more help, check out this quadratic formula solver.

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 4%2Ax%5E2-15%2Ax%2B9=0 ( notice a=4, b=-15, and c=9)





x+=+%28--15+%2B-+sqrt%28+%28-15%29%5E2-4%2A4%2A9+%29%29%2F%282%2A4%29 Plug in a=4, b=-15, and c=9




x+=+%2815+%2B-+sqrt%28+%28-15%29%5E2-4%2A4%2A9+%29%29%2F%282%2A4%29 Negate -15 to get 15




x+=+%2815+%2B-+sqrt%28+225-4%2A4%2A9+%29%29%2F%282%2A4%29 Square -15 to get 225 (note: remember when you square -15, you must square the negative as well. This is because %28-15%29%5E2=-15%2A-15=225.)




x+=+%2815+%2B-+sqrt%28+225%2B-144+%29%29%2F%282%2A4%29 Multiply -4%2A9%2A4 to get -144




x+=+%2815+%2B-+sqrt%28+81+%29%29%2F%282%2A4%29 Combine like terms in the radicand (everything under the square root)




x+=+%2815+%2B-+9%29%2F%282%2A4%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%2815+%2B-+9%29%2F8 Multiply 2 and 4 to get 8


So now the expression breaks down into two parts


x+=+%2815+%2B+9%29%2F8 or x+=+%2815+-+9%29%2F8


Lets look at the first part:


x=%2815+%2B+9%29%2F8


x=24%2F8 Add the terms in the numerator

x=3 Divide


So one answer is

x=3




Now lets look at the second part:


x=%2815+-+9%29%2F8


x=6%2F8 Subtract the terms in the numerator

x=3%2F4 Divide


So another answer is

x=3%2F4