SOLUTION: Solve the quadratic equation 4x²+28x-15=0

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Question 164512: Solve the quadratic equation
4x²+28x-15=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4x%5E2%2B28x-15=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=4, b=28, 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-%2828%29+%2B-+sqrt%28+%2828%29%5E2-4%284%29%28-15%29+%29%29%2F%282%284%29%29 Plug in a=4, b=28, and c=-15


x+=+%28-28+%2B-+sqrt%28+784-4%284%29%28-15%29+%29%29%2F%282%284%29%29 Square 28 to get 784.


x+=+%28-28+%2B-+sqrt%28+784--240+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-15%29 to get -240


x+=+%28-28+%2B-+sqrt%28+784%2B240+%29%29%2F%282%284%29%29 Rewrite sqrt%28784--240%29 as sqrt%28784%2B240%29


x+=+%28-28+%2B-+sqrt%28+1024+%29%29%2F%282%284%29%29 Add 784 to 240 to get 1024


x+=+%28-28+%2B-+sqrt%28+1024+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%28-28+%2B-+32%29%2F%288%29 Take the square root of 1024 to get 32.


x+=+%28-28+%2B+32%29%2F%288%29 or x+=+%28-28+-+32%29%2F%288%29 Break up the expression.


x+=+%284%29%2F%288%29 or x+=++%28-60%29%2F%288%29 Combine like terms.


x+=+1%2F2 or x+=+-15%2F2 Simplify.


So the answers are x+=+1%2F2 or x+=+-15%2F2