SOLUTION: solve by completing the square. Check Both roots. x^2-x=3/4 2x^2-9x-5=0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: solve by completing the square. Check Both roots. x^2-x=3/4 2x^2-9x-5=0      Log On


   

Question 67257: solve by completing the square. Check Both roots.
x^2-x=3/4
2x^2-9x-5=0
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+-+x+=+3%2F4
take 1/2 of the coefficient of x, square it, and add it to both sides
x%5E2+-+x+%2B+%281%2F4%29+=+1
%28x+-+%281%2F2%29%29%5E2+=+1
x+-+%281%2F2%29+=+%2B1
x+-+%281%2F2%29+=+-1
x+=+3%2F2
x+=+-%281%2F2%29
check
x%5E2+-+x+=+3%2F4
%283%2F2%29%5E2+-+%283%2F2%29+=+3%2F4
%289%2F4%29+-+%286%2F4%29+=+3%2F4
3%2F4+=+3%2F4
%28-1%2F2%29%5E2+-%28-1%2F2%29+=+3%2F4
%281%2F4%29+%2B+%282%2F4%29+=+3%2F4
3%2F4+=+3%2F4
OK
2x%5E2+-+9x+-+5+=+0
x%5E2+-+%289%2F2%29x+=+5
x%5E2+-+%289%2F2%29x+%2B+%2881%2F16%29+=+%2880%2F16%29+%2B+%2881%2F16%29
x%5E2+-+%289%2F2%29x+%2B+%2881%2F16%29+=+161%2F16
%28x+-+9%2F4%29%5E2+=+%28161%2F16%29
x+-+%289%2F4%29+=+%28%2Bsqrt%28161%29+%2F+4%29
x+-+%289%2F4%29+=+%28-sqrt%28161%29+%2F+4%29
x+=+%289+%2B+sqrt%28161%29%29+%2F+4
x+=+%289+-+sqrt%28161%29%29+%2F+4
check
2x%5E2+-+9x+-+5+=+0
2%28%289+%2B+sqrt%28161%29%29+%2F+4%29%5E2+-+9%28%289+%2B+sqrt%28161%29%29+%2F+4%29+-+5+=+0
this is really hard for me to check
I possibly made a mistake, but you get the idea