SOLUTION: complete the square 2m^2-m-15=0 using the quadratic formula 2y^2-3y-6=0

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Question 726631: complete the square
2m^2-m-15=0
using the quadratic formula
2y^2-3y-6=0
Found 2 solutions by tanjo3, lwsshak3:
Answer by tanjo3(60) About Me  (Show Source):
You can put this solution on YOUR website!
Part 1:
2m%5E2+-+m+-+15+=+0
2m%5E2+-+m+=+15
m%5E2+-+%281%2F2%29m+-+15%2F2+=+15%2F2
m%5E2+-+%281%2F2%29m+%2B+1%2F16+-+1%2F16+-+15%2F2+=+0
m%5E2+-+%281%2F2%29m+%2B+1%2F16+-+1%2F16+-+120%2F16+=+0
m%5E2+-+%281%2F2%29m+%2B+1%2F16+-+121%2F16+=+0
%28m+-+1%2F4%29%5E2+-+121%2F16+=+0
Part 2:
2y%5E2+-+3y+-+6=0
y+=+%28-b+%2B-+sqrt%28b%5E2-4%2Aa%2Ac%29%29%2F%282%2Aa%29
y+=+%283+%2B-+sqrt%28%28-3%29%5E2-4%2A2%2A%28-6%29%29%29%2F%282%2A2%29
y+=+%283+%2B-+sqrt%2857%29%29%2F4

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
complete the square
2m^2-m-15=0
2(m^2-m/2+1/16)=15+1/8=120/8+1/8=121/8
2(m-1/4)^2=121/8
divide both sides by 2
(m-1/4)^2=121/16
take sqrt of both sides
m-1/4=±11/4
m=1/4±11/4
m=1/4+11/4=3
or
m=1/4-11/4=-10/4=-5/2=-2.5
..
using the quadratic formula
2y^2-3y-6=0
quadratic formula:
y=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=2, b=-3, c=-6
y={-(-3)±√(-3)^2-4*2*-6)}/(2*2)
=[3±√(9+48)]/4
=(3±√57)/4
y=(3+√57)/4
or
y=(3-√57)/4