SOLUTION: What is 4a^2-28a=-49?

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Question 236636: What is 4a^2-28a=-49?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4a%5E2-28a=-49 Start with the given equation.


4a%5E2-28a%2B49=0 Add 49 to both sides.


Notice that the quadratic 4a%5E2-28a%2B49 is in the form of Aa%5E2%2BBa%2BC where A=4, B=-28, and C=49


Let's use the quadratic formula to solve for "a":


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


a+=+%28-%28-28%29+%2B-+sqrt%28+%28-28%29%5E2-4%284%29%2849%29+%29%29%2F%282%284%29%29 Plug in A=4, B=-28, and C=49


a+=+%2828+%2B-+sqrt%28+%28-28%29%5E2-4%284%29%2849%29+%29%29%2F%282%284%29%29 Negate -28 to get 28.


a+=+%2828+%2B-+sqrt%28+784-4%284%29%2849%29+%29%29%2F%282%284%29%29 Square -28 to get 784.


a+=+%2828+%2B-+sqrt%28+784-784+%29%29%2F%282%284%29%29 Multiply 4%284%29%2849%29 to get 784


a+=+%2828+%2B-+sqrt%28+0+%29%29%2F%282%284%29%29 Subtract 784 from 784 to get 0


a+=+%2828+%2B-+sqrt%28+0+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


a+=+%2828+%2B-+0%29%2F%288%29 Take the square root of 0 to get 0.


a+=+%2828+%2B+0%29%2F%288%29 or a+=+%2828+-+0%29%2F%288%29 Break up the expression.


a+=+%2828%29%2F%288%29 or a+=++%2828%29%2F%288%29 Combine like terms.


a+=+7%2F2 or a+=+7%2F2 Simplify.


So the solution is a+=+7%2F2