SOLUTION: (2x+3)^1.8=250 help please

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Question 298010: (2x+3)^1.8=250
help please
Found 3 solutions by JBarnum, richwmiller, MathTherapy:
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
%282x%2B3%29%5E1.8=250
%282x%2B3%29%28.8%282x%2B3%29%29=250
%282x%2B3%29%281.6x%2B2.4%29=250
%283.2x%5E2%2B4.8x%2B4.8x%2B7.2%29=250
%283.2x%5E2%2B9.6x%2B7.2%29=250
3.2x%5E2%2B9.6x-242.8=0
3.2%28x%5E2%2B3x-75.875%29=0use quadratic formula
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-75.875+=+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=%283%29%5E2-4%2A1%2A-75.875=312.5.

Discriminant d=312.5 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+312.5+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+312.5+%29%29%2F2%5C1+=+7.33883476483184
x%5B2%5D+=+%28-%283%29-sqrt%28+312.5+%29%29%2F2%5C1+=+-10.3388347648318

Quadratic expression 1x%5E2%2B3x%2B-75.875 can be factored:
1x%5E2%2B3x%2B-75.875+=+1%28x-7.33883476483184%29%2A%28x--10.3388347648318%29
Again, the answer is: 7.33883476483184, -10.3388347648318. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-75.875+%29

hmmm looking at this after i posted seems to be something wrong i would check with someone else sorry

Answer by richwmiller(17219) About Me  (Show Source):
Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
%282x+%2B+3%29%5E1.8+=+250

Raise each side of equation to the 1%2F1.8th power to get rid of the 1.8 exponent on the left-side. This gives us:

%282x+%2B+3%29%5E%281.8%2A%281%2F1.8%29%29+=+250%5E%281%2F1.8%29 ------> %282x+%2B+3%29+=+250%5E%281%2F1.8%29, or, %282x+%2B+3%29+=+250%5E.5556 -----> 2x+%2B+3+=+21.48764863

2x = 18.48764863

x = 18.48764863%2F2 ------> highlight_green%28x+=+9.243824315%29

It CHECKS out but I'll still leave it for you to check. Okay?