Question 722289
1. {{{2m^2 - m - 15 = 0}}}
these are based on the form y = ax^2 + bx + c
In this equation a=2; b=-1; c=-15
:
the Quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
in our equation x=m; a=2; b=-1; c= -15
{{{m = (-(-1) +- sqrt(-1^2-4*2*-15 ))/(2*2) }}}
do the math
{{{m = (1 +- sqrt(1+120 ))/(4) }}}
{{{m = (1 +- sqrt(121 ))/(4) }}}
two solution from the square root of 121
{{{m = (1 + 11)/(4) }}}
m = {{{12/4}}}
m = 3
and
{{{m = (1 - 11)/(4) }}} 
m = -10/4
m = -2.5
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factoring
{{{2m^2 - m - 15 = 0}}}
(2m ___)(m____) = 0
find the two factors of -15 that when you FOIL them the middle coefficient is -1
(2m + 5)(m - 3) = 0
Same solutions
2m = -5
m = -5/2 (-2.5)
and
m = +3 
:
Completing the square, write it
{{{2m^2 - m + __ = 15}}}
when completing the square, the coefficient of m^2 has to be 1, 
divide thru by 2 
m^2 - .5m + ___ = 7.5
Find the value that completes the square,
 divide the coefficient of m and square it, that's (.5/2)^2 = .0625, 
add to both sides
m^2 -.5m + .0625 = 7.5 + .0625
m^2 - .5m + .0625 = 7.5625
Which is
(m - .25)^2 = 7.5625
Find the square root of both sides
m - .25 = +/-{{{sqrt(7.625)}}}
m = .25 +/-{{{sqrt(7.625)}}}
Find the square root,  you have two solutions
m = .25 + 2.75
m = 3
and
m = .25 - 2.75
m = -2.5 
:
Discriminant: D = b^2 - 4*a*c, remember a=2; b=-1; c=-15
D = -1^2 - 4 * 2 * -15
D = 1 + 120
D = 121
It's positive, therefore, there are two unequal real roots, (which we knew) 
:
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I only have time for one of these, using this try to do the next one yourself





2. 2y^(2) - 3y - 6 = 0