SOLUTION: (2x)x + 5x - 3 = 294

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Question 159348: (2x)x + 5x - 3 = 294
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%282x%29x+%2B+5x+-+3+=+294 Start with the given equation


2x%5E2+%2B+5x+-+3+=+294 Multiply


2x%5E2+%2B+5x+-+3+-+294=0 Subtract 294 from both sides


2x%5E2+%2B+5x+-297=0 Subtract


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=2, b=5, and c=-297


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-%285%29+%2B-+sqrt%28+%285%29%5E2-4%282%29%28-297%29+%29%29%2F%282%282%29%29 Plug in a=2, b=5, and c=-297


x+=+%28-5+%2B-+sqrt%28+25-4%282%29%28-297%29+%29%29%2F%282%282%29%29 Square 5 to get 25.


x+=+%28-5+%2B-+sqrt%28+25--2376+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-297%29 to get -2376


x+=+%28-5+%2B-+sqrt%28+25%2B2376+%29%29%2F%282%282%29%29 Rewrite sqrt%2825--2376%29 as sqrt%2825%2B2376%29


x+=+%28-5+%2B-+sqrt%28+2401+%29%29%2F%282%282%29%29 Add 25 to 2376 to get 2401


x+=+%28-5+%2B-+sqrt%28+2401+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%28-5+%2B-+49%29%2F%284%29 Take the square root of 2401 to get 49.


x+=+%28-5+%2B+49%29%2F%284%29 or x+=+%28-5+-+49%29%2F%284%29 Break up the expression.


x+=+%2844%29%2F%284%29 or x+=++%28-54%29%2F%284%29 Combine like terms.


x+=+11 or x+=+-27%2F2 Simplify.


So the answers are x+=+11 or x+=+-27%2F2