SOLUTION: Solve the quadratic equation: a^2-3a-28=0

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Question 318391: Solve the quadratic equation: a^2-3a-28=0
Found 2 solutions by solver91311, jim_thompson5910:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


4 times -7 is -28
4 plus -7 is -3


John

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

a%5E2-3a-28=0 Start with the given equation.


Notice that the quadratic a%5E2-3a-28 is in the form of Aa%5E2%2BBa%2BC where A=1, B=-3, and C=-28


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-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%28-28%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-3, and C=-28


a+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%28-28%29+%29%29%2F%282%281%29%29 Negate -3 to get 3.


a+=+%283+%2B-+sqrt%28+9-4%281%29%28-28%29+%29%29%2F%282%281%29%29 Square -3 to get 9.


a+=+%283+%2B-+sqrt%28+9--112+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-28%29 to get -112


a+=+%283+%2B-+sqrt%28+9%2B112+%29%29%2F%282%281%29%29 Rewrite sqrt%289--112%29 as sqrt%289%2B112%29


a+=+%283+%2B-+sqrt%28+121+%29%29%2F%282%281%29%29 Add 9 to 112 to get 121


a+=+%283+%2B-+sqrt%28+121+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


a+=+%283+%2B-+11%29%2F%282%29 Take the square root of 121 to get 11.


a+=+%283+%2B+11%29%2F%282%29 or a+=+%283+-+11%29%2F%282%29 Break up the expression.


a+=+%2814%29%2F%282%29 or a+=++%28-8%29%2F%282%29 Combine like terms.


a+=+7 or a+=+-4 Simplify.


So the solutions are a+=+7 or a+=+-4