SOLUTION: i need help solving these quadratic equations using the quadratic formula. 2x^2 - 5x = 3

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: i need help solving these quadratic equations using the quadratic formula. 2x^2 - 5x = 3       Log On


   

Question 107050: i need help solving these quadratic equations using the quadratic formula.
2x^2 - 5x = 3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E2+-+5x+=+3+ Start with the given equation


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


Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 2%2Ax%5E2-5%2Ax-3=0 ( notice a=2, b=-5, and c=-3)





x+=+%28--5+%2B-+sqrt%28+%28-5%29%5E2-4%2A2%2A-3+%29%29%2F%282%2A2%29 Plug in a=2, b=-5, and c=-3




x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%2A2%2A-3+%29%29%2F%282%2A2%29 Negate -5 to get 5




x+=+%285+%2B-+sqrt%28+25-4%2A2%2A-3+%29%29%2F%282%2A2%29 Square -5 to get 25 (note: remember when you square -5, you must square the negative as well. This is because %28-5%29%5E2=-5%2A-5=25.)




x+=+%285+%2B-+sqrt%28+25%2B24+%29%29%2F%282%2A2%29 Multiply -4%2A-3%2A2 to get 24




x+=+%285+%2B-+sqrt%28+49+%29%29%2F%282%2A2%29 Combine like terms in the radicand (everything under the square root)




x+=+%285+%2B-+7%29%2F%282%2A2%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%285+%2B-+7%29%2F4 Multiply 2 and 2 to get 4


So now the expression breaks down into two parts


x+=+%285+%2B+7%29%2F4 or x+=+%285+-+7%29%2F4


Lets look at the first part:


x=%285+%2B+7%29%2F4


x=12%2F4 Add the terms in the numerator

x=3 Divide


So one answer is

x=3




Now lets look at the second part:


x=%285+-+7%29%2F4


x=-2%2F4 Subtract the terms in the numerator

x=-1%2F2 Divide


So another answer is

x=-1%2F2


So our solutions are:

x=3 or x=-1%2F2