# Solve for m 12m^2+44m+45=0

12m2+44m+45=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=12, b=44, and c=45 into the quadratic formula and solve for m.
-44±442-4⋅(12⋅45)2⋅12
Simplify.
Simplify the numerator.
Raise 44 to the power of 2.
m=-44±1936-4⋅(12⋅45)2⋅12
Multiply 12 by 45.
m=-44±1936-4⋅5402⋅12
Multiply -4 by 540.
m=-44±1936-21602⋅12
Subtract 2160 from 1936.
m=-44±-2242⋅12
Rewrite -224 as -1(224).
m=-44±-1⋅2242⋅12
Rewrite -1(224) as -1⋅224.
m=-44±-1⋅2242⋅12
Rewrite -1 as i.
m=-44±i⋅2242⋅12
Rewrite 224 as 42⋅14.
Factor 16 out of 224.
m=-44±i⋅16(14)2⋅12
Rewrite 16 as 42.
m=-44±i⋅42⋅142⋅12
m=-44±i⋅42⋅142⋅12
Pull terms out from under the radical.
m=-44±i⋅(414)2⋅12
Move 4 to the left of i.
m=-44±4i142⋅12
m=-44±4i142⋅12
Multiply 2 by 12.
m=-44±4i1424
Simplify -44±4i1424.
m=-11±i146
m=-11±i146
The final answer is the combination of both solutions.
m=-11-i146,-11+i146
Solve for m 12m^2+44m+45=0

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