SOLUTION: 2x^2-24x=180 how do I get rid of the exponent so I can find the value of x?

Algebra ->  Angles -> SOLUTION: 2x^2-24x=180 how do I get rid of the exponent so I can find the value of x?      Log On


   

Question 997140: 2x^2-24x=180 how do I get rid of the exponent so I can find the value of x?
Found 2 solutions by Alan3354, josgarithmetic:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
2x^2-24x=180
x^2 - 12x - 90 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-12x%2B-90+=+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=%28-12%29%5E2-4%2A1%2A-90=504.

Discriminant d=504 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--12%2B-sqrt%28+504+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-12%29%2Bsqrt%28+504+%29%29%2F2%5C1+=+17.2249721603218
x%5B2%5D+=+%28-%28-12%29-sqrt%28+504+%29%29%2F2%5C1+=+-5.22497216032182

Quadratic expression 1x%5E2%2B-12x%2B-90 can be factored:
1x%5E2%2B-12x%2B-90+=+%28x-17.2249721603218%29%2A%28x--5.22497216032182%29
Again, the answer is: 17.2249721603218, -5.22497216032182. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-12%2Ax%2B-90+%29

Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
You do NOT get rid of the exponent.

Simplify and try to factorize.

x%5E2-12x=90
x%5E2-12x-90=0, factors in prime form for the constant, 3*3*2*5, and you might find in there, 6*15, something to test-try.

?
(x___6)(x____15)------no ; not work.
?
5*18 neither will work.

Discriminant?
%28-12%29%5E2-4%2A1%2A%28-90%29
144%2B360
504, not a perfect square, but a positive value.

Factorization will basically "not" work.
Formula for general solution to a quadratic equation gives
x=%2812%2B-+sqrt%28504%29%29%2F2

x=%2812%2B-+2%2Asqrt%28126%29%29%2F2

highlight%28x=6%2B-+sqrt%28126%29%29
or
highlight%28highlight%28x=6%2B-+3%2Asqrt%282%2A7%29%29%29