SOLUTION: 4x squared=14x+8 Please help Parent of student

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Question 420024: 4x squared=14x+8 Please help Parent of student
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4x%5E2=14x%2B8 Start with the given equation.


4x%5E2-14x-8=0 Get all terms to the left side.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=4, b=-14, and c=-8


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-%28-14%29+%2B-+sqrt%28+%28-14%29%5E2-4%284%29%28-8%29+%29%29%2F%282%284%29%29 Plug in a=4, b=-14, and c=-8


x+=+%2814+%2B-+sqrt%28+%28-14%29%5E2-4%284%29%28-8%29+%29%29%2F%282%284%29%29 Negate -14 to get 14.


x+=+%2814+%2B-+sqrt%28+196-4%284%29%28-8%29+%29%29%2F%282%284%29%29 Square -14 to get 196.


x+=+%2814+%2B-+sqrt%28+196--128+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-8%29 to get -128


x+=+%2814+%2B-+sqrt%28+196%2B128+%29%29%2F%282%284%29%29 Rewrite sqrt%28196--128%29 as sqrt%28196%2B128%29


x+=+%2814+%2B-+sqrt%28+324+%29%29%2F%282%284%29%29 Add 196 to 128 to get 324


x+=+%2814+%2B-+sqrt%28+324+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%2814+%2B-+18%29%2F%288%29 Take the square root of 324 to get 18.


x+=+%2814+%2B+18%29%2F%288%29 or x+=+%2814+-+18%29%2F%288%29 Break up the expression.


x+=+%2832%29%2F%288%29 or x+=++%28-4%29%2F%288%29 Combine like terms.


x+=+4 or x+=+-1%2F2 Simplify.


So the answers are x+=+4 or x+=+-1%2F2


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