Solve for m m^3=8

m3=8
Move 8 to the left side of the equation by subtracting it from both sides.
m3-8=0
Factor the left side of the equation.
Rewrite 8 as 23.
m3-23=0
Since both terms are perfect cubes, factor using the difference of cubes formula, a3-b3=(a-b)(a2+ab+b2) where a=m and b=2.
(m-2)(m2+m⋅2+22)=0
Simplify.
Move 2 to the left of m.
(m-2)(m2+2m+22)=0
Raise 2 to the power of 2.
(m-2)(m2+2m+4)=0
(m-2)(m2+2m+4)=0
(m-2)(m2+2m+4)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
m-2=0
m2+2m+4=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
m-2=0
Add 2 to both sides of the equation.
m=2
m=2
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
m2+2m+4=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=2, and c=4 into the quadratic formula and solve for m.
-2±22-4⋅(1⋅4)2⋅1
Simplify.
Simplify the numerator.
Raise 2 to the power of 2.
m=-2±4-4⋅(1⋅4)2⋅1
Multiply 4 by 1.
m=-2±4-4⋅42⋅1
Multiply -4 by 4.
m=-2±4-162⋅1
Subtract 16 from 4.
m=-2±-122⋅1
Rewrite -12 as -1(12).
m=-2±-1⋅122⋅1
Rewrite -1(12) as -1⋅12.
m=-2±-1⋅122⋅1
Rewrite -1 as i.
m=-2±i⋅122⋅1
Rewrite 12 as 22⋅3.
Factor 4 out of 12.
m=-2±i⋅4(3)2⋅1
Rewrite 4 as 22.
m=-2±i⋅22⋅32⋅1
m=-2±i⋅22⋅32⋅1
Pull terms out from under the radical.
m=-2±i⋅(23)2⋅1
Move 2 to the left of i.
m=-2±2i32⋅1
m=-2±2i32⋅1
Multiply 2 by 1.
m=-2±2i32
Simplify -2±2i32.
m=-1±i3
m=-1±i3
The final answer is the combination of both solutions.
m=-1+i3,-1-i3
m=-1+i3,-1-i3
The final solution is all the values that make (m-2)(m2+2m+4)=0 true.
m=2,-1+i3,-1-i3
Solve for m m^3=8

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