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

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Question 394818: solve 2x^2-2x=3
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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


2x%5E2-2x-3=0 Subtract 3 from both sides.


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


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


x+=+%282+%2B-+sqrt%28+%28-2%29%5E2-4%282%29%28-3%29+%29%29%2F%282%282%29%29 Negate -2 to get 2.


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


x+=+%282+%2B-+sqrt%28+4--24+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-3%29 to get -24


x+=+%282+%2B-+sqrt%28+4%2B24+%29%29%2F%282%282%29%29 Rewrite sqrt%284--24%29 as sqrt%284%2B24%29


x+=+%282+%2B-+sqrt%28+28+%29%29%2F%282%282%29%29 Add 4 to 24 to get 28


x+=+%282+%2B-+sqrt%28+28+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%282+%2B-+2%2Asqrt%287%29%29%2F%284%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%282%2B2%2Asqrt%287%29%29%2F%284%29 or x+=+%282-2%2Asqrt%287%29%29%2F%284%29 Break up the expression.


x+=+%281%2Bsqrt%287%29%29%2F%282%29 or x+=+%281-sqrt%287%29%29%2F%282%29 Reduce


So the solutions are x+=+%281%2Bsqrt%287%29%29%2F%282%29 or x+=+%281-sqrt%287%29%29%2F%282%29


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
2x^2-2x=3
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2x^2-2x-3 = 0
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x = [2 +- sqrt(4-4*2*-3)]/4
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x = [2 +- sqrt(28)]/4
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x = [2 +- 2sqrt(7)]/4
----
x = [1 +- sqrt(7)]/2
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Cheers,
Stan H.