SOLUTION: Use the quadratic equation to solve 2x^2-5x=-9 Use i if complex answer. i would appreciate a breakdown of the solution..Thanks

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Question 156773: Use the quadratic equation to solve
2x^2-5x=-9
Use i if complex answer.
i would appreciate a breakdown of the solution..Thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2-5x=-9 Start with the given equation.


2x%5E2-5x%2B9=0 Add 9 to both sides.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=2, b=-5, and c=9


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-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%282%29%289%29+%29%29%2F%282%282%29%29 Plug in a=2, b=-5, and c=9


x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%282%29%289%29+%29%29%2F%282%282%29%29 Negate -5 to get 5.


x+=+%285+%2B-+sqrt%28+25-4%282%29%289%29+%29%29%2F%282%282%29%29 Square -5 to get 25.


x+=+%285+%2B-+sqrt%28+25-72+%29%29%2F%282%282%29%29 Multiply 4%282%29%289%29 to get 72


x+=+%285+%2B-+sqrt%28+-47+%29%29%2F%282%282%29%29 Subtract 72 from 25 to get -47


x+=+%285+%2B-+sqrt%28+-47+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%285+%2B-+i%2Asqrt%2847%29%29%2F%284%29 Simplify the square root


x+=+%285%2Bi%2Asqrt%2847%29%29%2F%284%29 or x+=+%285-i%2Asqrt%2847%29%29%2F%284%29 Break up the expression.


So the answers are x+=+%285%2Bi%2Asqrt%2847%29%29%2F%284%29 or x+=+%285-i%2Asqrt%2847%29%29%2F%284%29


which approximate to x=1.25%2B1.714%2Ai or x=1.25%2B1.714%2Ai