SOLUTION: solve 2x^2 - 3x - 2 = 0 using quadratic formula

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Question 200227: solve
2x^2 - 3x - 2 = 0 using quadratic formula
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2-3x-2=0 Start with the given equation.


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


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


x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%282%29%28-2%29+%29%29%2F%282%282%29%29 Negate -3 to get 3.


x+=+%283+%2B-+sqrt%28+9-4%282%29%28-2%29+%29%29%2F%282%282%29%29 Square -3 to get 9.


x+=+%283+%2B-+sqrt%28+9--16+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-2%29 to get -16


x+=+%283+%2B-+sqrt%28+9%2B16+%29%29%2F%282%282%29%29 Rewrite sqrt%289--16%29 as sqrt%289%2B16%29


x+=+%283+%2B-+sqrt%28+25+%29%29%2F%282%282%29%29 Add 9 to 16 to get 25


x+=+%283+%2B-+sqrt%28+25+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%283+%2B-+5%29%2F%284%29 Take the square root of 25 to get 5.


x+=+%283+%2B+5%29%2F%284%29 or x+=+%283+-+5%29%2F%284%29 Break up the expression.


x+=+%288%29%2F%284%29 or x+=++%28-2%29%2F%284%29 Combine like terms.


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


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