Question 695875
Quadratic formula is {{{x=(-b+-sqrt(b^2-4ac))/2a}}}
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Using {{{3m^2+m-2=0}}}, a is 3, b is 1 and c is -2
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{{{m=(-1+-sqrt(1^2-4(3)(-2)))/(2*3)}}}
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{{{m = (-1+-sqrt(1+24))/(6)}}}
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{{{m = (-1+-5)/6}}}
Two solutions
m = {{{(-1+5)/6}}}, so {{{highlight_green(m = 4/6 = 2/3)}}}
m = {{{(-1-5)/6}}}, so {{{highlight_green(m = -6/6 = -1)}}}
The solutions make sense because it factors as (3m-2)(m+1)=0
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Using 5p^2 + 3p - 2 = 0
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{{{p =(-3+-sqrt(3^2-4(5)(-2)))/(2*5)}}}
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{{{p = (-3+-sqrt(9+40))/10}}}
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{{{p = (-3+-7)/10}}}
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Two solutions
p = {{{(-3+7)/10}}}, so {{{highlight_green(p = 4/10 = 2/5)}}}
p = {{{(-3-7)/10}}}, so {{{highlight_green(p = -10/10 = -1)}}}
The solutions make sense because it factors as (5p-2)(p+1)=0
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