SOLUTION: 2x²-x=15

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Question 183093: 2x²-x=15
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2-x=15 Start with the given equation.


2x%5E2-x-15=0 Subtract 15 from both sides.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=2, b=-1, and c=-15


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%282%29%28-15%29+%29%29%2F%282%282%29%29 Plug in a=2, b=-1, and c=-15


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%282%29%28-15%29+%29%29%2F%282%282%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%282%29%28-15%29+%29%29%2F%282%282%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1--120+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-15%29 to get -120


x+=+%281+%2B-+sqrt%28+1%2B120+%29%29%2F%282%282%29%29 Rewrite sqrt%281--120%29 as sqrt%281%2B120%29


x+=+%281+%2B-+sqrt%28+121+%29%29%2F%282%282%29%29 Add 1 to 120 to get 121


x+=+%281+%2B-+sqrt%28+121+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%281+%2B-+11%29%2F%284%29 Take the square root of 121 to get 11.


x+=+%281+%2B+11%29%2F%284%29 or x+=+%281+-+11%29%2F%284%29 Break up the expression.


x+=+%2812%29%2F%284%29 or x+=++%28-10%29%2F%284%29 Combine like terms.


x+=+3 or x+=+-5%2F2 Simplify.


So the answers are x+=+3 or x+=+-5%2F2