SOLUTION: Solve. Round results to the nearest thousandth. x^2 + 8x - 33 = 0

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Question 157084: Solve. Round results to the nearest thousandth.
x^2 + 8x - 33 = 0

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

x%5E2%2B8x-33=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=8, and c=-33


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-%288%29+%2B-+sqrt%28+%288%29%5E2-4%281%29%28-33%29+%29%29%2F%282%281%29%29 Plug in a=1, b=8, and c=-33


x+=+%28-8+%2B-+sqrt%28+64-4%281%29%28-33%29+%29%29%2F%282%281%29%29 Square 8 to get 64.


x+=+%28-8+%2B-+sqrt%28+64--132+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-33%29 to get -132


x+=+%28-8+%2B-+sqrt%28+64%2B132+%29%29%2F%282%281%29%29 Rewrite sqrt%2864--132%29 as sqrt%2864%2B132%29


x+=+%28-8+%2B-+sqrt%28+196+%29%29%2F%282%281%29%29 Add 64 to 132 to get 196


x+=+%28-8+%2B-+sqrt%28+196+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-8+%2B-+14%29%2F%282%29 Take the square root of 196 to get 14.


x+=+%28-8+%2B+14%29%2F%282%29 or x+=+%28-8+-+14%29%2F%282%29 Break up the expression.


x+=+%286%29%2F%282%29 or x+=++%28-22%29%2F%282%29 Combine like terms.


x+=+3 or x+=+-11 Simplify.


So the answers are x+=+3 or x+=+-11