SOLUTION: solve. 2x^2=5-3x

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Question 581832: solve. 2x^2=5-3x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2=5-3x Start with the given equation.


2x%5E2-5%2B3x=0 Get every term to the left side.


2x%5E2%2B3x-5=0 Rearrange the terms.


Notice that the quadratic 2x%5E2%2B3x-5 is in the form of Ax%5E2%2BBx%2BC where A=2, B=3, and C=-5


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-%283%29+%2B-+sqrt%28+%283%29%5E2-4%282%29%28-5%29+%29%29%2F%282%282%29%29 Plug in A=2, B=3, and C=-5


x+=+%28-3+%2B-+sqrt%28+9-4%282%29%28-5%29+%29%29%2F%282%282%29%29 Square 3 to get 9.


x+=+%28-3+%2B-+sqrt%28+9--40+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-5%29 to get -40


x+=+%28-3+%2B-+sqrt%28+9%2B40+%29%29%2F%282%282%29%29 Rewrite sqrt%289--40%29 as sqrt%289%2B40%29


x+=+%28-3+%2B-+sqrt%28+49+%29%29%2F%282%282%29%29 Add 9 to 40 to get 49


x+=+%28-3+%2B-+sqrt%28+49+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%28-3+%2B-+7%29%2F%284%29 Take the square root of 49 to get 7.


x+=+%28-3+%2B+7%29%2F%284%29 or x+=+%28-3+-+7%29%2F%284%29 Break up the expression.


x+=+%284%29%2F%284%29 or x+=++%28-10%29%2F%284%29 Combine like terms.


x+=+1 or x+=+-5%2F2 Simplify.


So the solutions are x+=+1 or x+=+-5%2F2