SOLUTION: Can you please help me with this equation {{{2x^2-3x-5=0}}}

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Question 200197This question is from textbook Mathematics in Our World
: Can you please help me with this equation
2x%5E2-3x-5=0 This question is from textbook Mathematics in Our World

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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


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


x+=+%283+%2B-+sqrt%28+9-4%282%29%28-5%29+%29%29%2F%282%282%29%29 Square -3 to get 9.


x+=+%283+%2B-+sqrt%28+9--40+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-5%29 to get -40


x+=+%283+%2B-+sqrt%28+9%2B40+%29%29%2F%282%282%29%29 Rewrite sqrt%289--40%29 as sqrt%289%2B40%29


x+=+%283+%2B-+sqrt%28+49+%29%29%2F%282%282%29%29 Add 9 to 40 to get 49


x+=+%283+%2B-+sqrt%28+49+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%283+%2B-+7%29%2F%284%29 Take the square root of 49 to get 7.


x+=+%283+%2B+7%29%2F%284%29 or x+=+%283+-+7%29%2F%284%29 Break up the expression.


x+=+%2810%29%2F%284%29 or x+=++%28-4%29%2F%284%29 Combine like terms.


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


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