Question 188824
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 + {{{5/2}}}x - 4 = 0
:
x^2 + {{{5/2}}}x + ___ = 4
Choose a value that will complete the square
Take half the coefficient of x and square it to accomplish this:
 {{{(1/2)*(5/2) = (5/4)}}}Square this and you have {{{25/16}}}, add to both sides
x^2 + {{{5/2}}}x + {{{25/16}}} =  4 + {{{25/16}}}
x^2 + {{{5/2}}}x + {{{25/16}}} =  {{{64/16}}} + {{{25/16}}} 
x^2 + {{{5/2}}}x + {{{25/16}}} =  {{{89/16}}}
which is
(x + {{{5/4}}})^2 = {{{89/16}}}
Find the square root of both sides:
x + {{{5/4}}} = +/-{{{sqrt(89/16)}}}
:
x = {{{-5/4}}} +/- {{{sqrt(89/16)}}}
Extract the perfect square
x = {{{-5/4}}} +/- {{{(1/4)sqrt(89)}}}
:
x = {{{(-5 + sqrt(89))/4}}}
and
x = {{{(-5 - sqrt(89))/4}}}