SOLUTION: Solve using the quadratic formula: x^2-3x-23=5

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Question 184187: Solve using the quadratic formula:
x^2-3x-23=5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-3x-23=5 Start with the given equation.


x%5E2-3x-23-5=0 Subtract 5 from both sides.


x%5E2-3x-28=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-3, and c=-28


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-%28-3%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


x+=+%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.


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


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


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


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


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


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


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


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


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


So the answers are x+=+7 or x+=+-4