Question 137172
 2x^2 - x - 5 = 0
:
When you complete the square, you want the coefficient of x^2 to be 1, 
divide the equation by 2, to accomplish this
x^2 - {{{1/2}}}x - {{{5/2}}} = 0
:
Add {{{5/2}}} to both sides, leave a place for the value we need to complete the square
x^2 - {{{1/2}}}x + ___ = {{{5/2}}}
:
Find the third term by dividing the coefficient of x by 2 and squaring it:
Here that would be; {{{(1/4)^2}}} which is {{{1/8}}}, we now have:
x^2 - {{{1/2}}}x + {{{1/8}}} = {{{5/2}}} + {{{1/8}}}; we have to add {{{1/8}}}to both sides
x^2 - {{{1/2}}}x + {{{1/8}}} = {{{20/8}}} + {{{1/8}}}; find a common denominator so we cam add the fractions
x^2 - {{{1/2}}}x + {{{1/8}}} = {{{(21)/8}}}
We have perfect square which is:
(x - {{{1/4}}})^2 = {{{(21)/8}}}
Find the square root of both sides:
x - {{{1/4}}} = +/-{{{sqrt(21/8)}}}
we can extract the sqrt of 4 in the denominator;
x - {{{1/4}}} = +/-{{{(1/2)*sqrt(21/2)}}}
add 1/4 to both sides
x = {{{1/4}}}+/-{{{(1/2)*sqrt(21/2)}}}
or we can write it
x = {{{1/4}}}+/-{{{(2/4)*sqrt(21/2)}}}
Put it all over a denominator of 4
x = {{{(1 + 2*sqrt(21/2))/4}}}
and
x = {{{(1 - 2*sqrt(21/2))/4}}}
Didthishelp?