SOLUTION: 4x^2 + 4x +1 =16

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Question 554913: 4x^2 + 4x +1 =16
Answer by jim_thompson5910(35256) About Me  (Show Source):
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4x%5E2%2B4x%2B1=16 Start with the given equation.


4x%5E2%2B4x%2B1-16=0 Get every term to the left side.


4x%5E2%2B4x-15=0 Combine like terms.


Notice that the quadratic 4x%5E2%2B4x-15 is in the form of Ax%5E2%2BBx%2BC where A=4, B=4, 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-%284%29+%2B-+sqrt%28+%284%29%5E2-4%284%29%28-15%29+%29%29%2F%282%284%29%29 Plug in A=4, B=4, and C=-15


x+=+%28-4+%2B-+sqrt%28+16-4%284%29%28-15%29+%29%29%2F%282%284%29%29 Square 4 to get 16.


x+=+%28-4+%2B-+sqrt%28+16--240+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-15%29 to get -240


x+=+%28-4+%2B-+sqrt%28+16%2B240+%29%29%2F%282%284%29%29 Rewrite sqrt%2816--240%29 as sqrt%2816%2B240%29


x+=+%28-4+%2B-+sqrt%28+256+%29%29%2F%282%284%29%29 Add 16 to 240 to get 256


x+=+%28-4+%2B-+sqrt%28+256+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%28-4+%2B-+16%29%2F%288%29 Take the square root of 256 to get 16.


x+=+%28-4+%2B+16%29%2F%288%29 or x+=+%28-4+-+16%29%2F%288%29 Break up the expression.


x+=+%2812%29%2F%288%29 or x+=++%28-20%29%2F%288%29 Combine like terms.


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


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


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