SOLUTION: Solve the quadratic equation by completing the square. {{{ 2x^2 }}} + 5x - 8 = 0 Could you please provide me a detailed explanation of how to obtain the answer

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve the quadratic equation by completing the square. {{{ 2x^2 }}} + 5x - 8 = 0 Could you please provide me a detailed explanation of how to obtain the answer      Log On


   

Question 188824: Solve the quadratic equation by completing the square.
+2x%5E2+ + 5x - 8 = 0

Could you please provide me a detailed explanation of how to obtain the answer
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the quadratic equation by completing the square.
2x^2 + 5x - 8 = 0
:
We need to have the coefficient of x^2 equal 1, divide equation by 2
x^2 + 5%2F2x - 4 = 0
:
x^2 + 5%2F2x + ___ = 4
Choose a value that will complete the square
Take half the coefficient of x and square it to accomplish this:
%281%2F2%29%2A%285%2F2%29+=+%285%2F4%29Square this and you have 25%2F16, add to both sides
x^2 + 5%2F2x + 25%2F16 = 4 + 25%2F16
x^2 + 5%2F2x + 25%2F16 = 64%2F16 + 25%2F16
x^2 + 5%2F2x + 25%2F16 = 89%2F16
which is
(x + 5%2F4)^2 = 89%2F16
Find the square root of both sides:
x + 5%2F4 = +/-sqrt%2889%2F16%29
:
x = -5%2F4 +/- sqrt%2889%2F16%29
Extract the perfect square
x = -5%2F4 +/- %281%2F4%29sqrt%2889%29
:
x = %28-5+%2B+sqrt%2889%29%29%2F4
and
x = %28-5+-+sqrt%2889%29%29%2F4