m3=8

Move 8 to the left side of the equation by subtracting it from both sides.

m3-8=0

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.

m-2=0

Add 2 to both sides of the equation.

m=2

m=2

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