m2=m

Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.

m=m2

To remove the radical on the left side of the equation, square both sides of the equation.

m2=(m2)2

Multiply the exponents in (m12)2.

Apply the power rule and multiply exponents, (am)n=amn.

m12⋅2=(m2)2

Cancel the common factor of 2.

Cancel the common factor.

m12⋅2=(m2)2

Rewrite the expression.

m1=(m2)2

m1=(m2)2

m1=(m2)2

Simplify.

m=(m2)2

Multiply the exponents in (m2)2.

Apply the power rule and multiply exponents, (am)n=amn.

m=m2⋅2

Multiply 2 by 2.

m=m4

m=m4

m=m4

Subtract m4 from both sides of the equation.

m-m4=0

Factor the left side of the equation.

Factor m out of m-m4.

Raise m to the power of 1.

m-m4=0

Factor m out of m1.

m⋅1-m4=0

Factor m out of -m4.

m⋅1+m(-m3)=0

Factor m out of m⋅1+m(-m3).

m(1-m3)=0

m(1-m3)=0

Rewrite 1 as 13.

m(13-m3)=0

Since both terms are perfect cubes, factor using the difference of cubes formula, a3-b3=(a-b)(a2+ab+b2) where a=1 and b=m.

m((1-m)(12+1m+m2))=0

Factor.

Simplify.

One to any power is one.

m((1-m)(1+1m+m2))=0

Multiply m by 1.

m((1-m)(1+m+m2))=0

m((1-m)(1+m+m2))=0

Remove unnecessary parentheses.

m(1-m)(1+m+m2)=0

m(1-m)(1+m+m2)=0

m(1-m)(1+m+m2)=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=0

1-m=0

1+m+m2=0

Set the first factor equal to 0.

m=0

Set the next factor equal to 0 and solve.

Set the next factor equal to 0.

1-m=0

Subtract 1 from both sides of the equation.

-m=-1

Multiply each term in -m=-1 by -1

Multiply each term in -m=-1 by -1.

(-m)⋅-1=(-1)⋅-1

Multiply (-m)⋅-1.

Multiply -1 by -1.

1m=(-1)⋅-1

Multiply m by 1.

m=(-1)⋅-1

m=(-1)⋅-1

Multiply -1 by -1.

m=1

m=1

m=1

Set the next factor equal to 0 and solve.

Set the next factor equal to 0.

1+m+m2=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=1, b=1, and c=1 into the quadratic formula and solve for m.

-1±12-4⋅(1⋅1)2⋅1

Simplify.

Simplify the numerator.

One to any power is one.

m=-1±1-4⋅(1⋅1)2⋅1

Multiply 1 by 1.

m=-1±1-4⋅12⋅1

Multiply -4 by 1.

m=-1±1-42⋅1

Subtract 4 from 1.

m=-1±-32⋅1

Rewrite -3 as -1(3).

m=-1±-1⋅32⋅1

Rewrite -1(3) as -1⋅3.

m=-1±-1⋅32⋅1

Rewrite -1 as i.

m=-1±i32⋅1

m=-1±i32⋅1

Multiply 2 by 1.

m=-1±i32

m=-1±i32

The final answer is the combination of both solutions.

m=-1-i32,-1+i32

m=-1-i32,-1+i32

The final solution is all the values that make m(1-m)(1+m+m2)=0 true.

m=0,1,-1-i32,-1+i32

m=0,1,-1-i32,-1+i32

Solve for m m^2 = square root of m