SOLUTION: Solve for x: 3x^2+5x-7=x^2+8x+28

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Question 120219: Solve for x: 3x^2+5x-7=x^2+8x+28
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2%2B5x-7=x%5E2%2B8x%2B28 Start with the given equation


3x%5E2%2B5x-7-x%5E2-8x-28=0 Subtract x^2 from both sides. Subtract 8x from both sides. Subtract 28 from both sides.


2x%5E2-3x-35=0 Combine like terms

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 2%2Ax%5E2-3%2Ax-35=0 ( notice a=2, b=-3, and c=-35)




x+=+%28--3+%2B-+sqrt%28+%28-3%29%5E2-4%2A2%2A-35+%29%29%2F%282%2A2%29 Plug in a=2, b=-3, and c=-35



x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%2A2%2A-35+%29%29%2F%282%2A2%29 Negate -3 to get 3



x+=+%283+%2B-+sqrt%28+9-4%2A2%2A-35+%29%29%2F%282%2A2%29 Square -3 to get 9 (note: remember when you square -3, you must square the negative as well. This is because %28-3%29%5E2=-3%2A-3=9.)



x+=+%283+%2B-+sqrt%28+9%2B280+%29%29%2F%282%2A2%29 Multiply -4%2A-35%2A2 to get 280



x+=+%283+%2B-+sqrt%28+289+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)



x+=+%283+%2B-+17%29%2F%282%2A2%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%283+%2B-+17%29%2F4 Multiply 2 and 2 to get 4

So now the expression breaks down into two parts

x+=+%283+%2B+17%29%2F4 or x+=+%283+-+17%29%2F4

Lets look at the first part:

x=%283+%2B+17%29%2F4

x=20%2F4 Add the terms in the numerator
x=5 Divide

So one answer is
x=5



Now lets look at the second part:

x=%283+-+17%29%2F4

x=-14%2F4 Subtract the terms in the numerator
x=-7%2F2 Divide

So another answer is
x=-7%2F2

So our solutions are:
x=5 or x=-7%2F2