# Solve for m m^2 = square root of m 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
Simplify each side of the equation.
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
Solve for m.
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

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