SOLUTION: How do I use the quadratic formula in this problem that one solution ends up being a fraction? 2x2-7x=-5. I know you have to put it in standard form first which is 2x2+7x-5.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: How do I use the quadratic formula in this problem that one solution ends up being a fraction? 2x2-7x=-5. I know you have to put it in standard form first which is 2x2+7x-5.      Log On


   

Question 177144: How do I use the quadratic formula in this problem that one solution ends up being a fraction? 2x2-7x=-5. I know you have to put it in standard form first which is 2x2+7x-5.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%5E2-7x=-5 Start with the given equation.


2x%5E2-7x%2B5=0 Get all terms to the left side.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=2, b=-7, 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-%28-7%29+%2B-+sqrt%28+%28-7%29%5E2-4%282%29%285%29+%29%29%2F%282%282%29%29 Plug in a=2, b=-7, and c=5


x+=+%287+%2B-+sqrt%28+%28-7%29%5E2-4%282%29%285%29+%29%29%2F%282%282%29%29 Negate -7 to get 7.


x+=+%287+%2B-+sqrt%28+49-4%282%29%285%29+%29%29%2F%282%282%29%29 Square -7 to get 49.


x+=+%287+%2B-+sqrt%28+49-40+%29%29%2F%282%282%29%29 Multiply 4%282%29%285%29 to get 40


x+=+%287+%2B-+sqrt%28+9+%29%29%2F%282%282%29%29 Subtract 40 from 49 to get 9


x+=+%287+%2B-+sqrt%28+9+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%287+%2B-+3%29%2F%284%29 Take the square root of 9 to get 3.


x+=+%287+%2B+3%29%2F%284%29 or x+=+%287+-+3%29%2F%284%29 Break up the expression.


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


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


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