SOLUTION: Solve. 2x^2+2x-5=0

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Question 689013: Solve. 2x^2+2x-5=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2%2B2x-5=0 Start with the given equation.


Notice that the quadratic 2x%5E2%2B2x-5 is in the form of Ax%5E2%2BBx%2BC where A=2, B=2, 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-%282%29+%2B-+sqrt%28+%282%29%5E2-4%282%29%28-5%29+%29%29%2F%282%282%29%29 Plug in A=2, B=2, and C=-5


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


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


x+=+%28-2+%2B-+sqrt%28+4%2B40+%29%29%2F%282%282%29%29 Rewrite sqrt%284--40%29 as sqrt%284%2B40%29


x+=+%28-2+%2B-+sqrt%28+44+%29%29%2F%282%282%29%29 Add 4 to 40 to get 44


x+=+%28-2+%2B-+sqrt%28+44+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%28-2+%2B-+2%2Asqrt%2811%29%29%2F%284%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-2%2B2%2Asqrt%2811%29%29%2F%284%29 or x+=+%28-2-2%2Asqrt%2811%29%29%2F%284%29 Break up the expression.


x+=+%28-1%2Bsqrt%2811%29%29%2F%282%29 or x+=+%28-1-sqrt%2811%29%29%2F%282%29 Reduce


So the solutions are x+=+%28-1%2Bsqrt%2811%29%29%2F%282%29 or x+=+%28-1-sqrt%2811%29%29%2F%282%29