# Solve for m m+4=5 square root of m

m+4=5m
Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.
5m=m+4
To remove the radical on the left side of the equation, square both sides of the equation.
(5m)2=(m+4)2
Simplify each side of the equation.
Apply the product rule to 5m12.
52(m12)2=(m+4)2
Raise 5 to the power of 2.
25(m12)2=(m+4)2
Multiply the exponents in (m12)2.
Apply the power rule and multiply exponents, (am)n=amn.
25m12⋅2=(m+4)2
Cancel the common factor of 2.
Cancel the common factor.
25m12⋅2=(m+4)2
Rewrite the expression.
25m1=(m+4)2
25m1=(m+4)2
25m1=(m+4)2
Simplify.
25m=(m+4)2
25m=(m+4)2
Solve for m.
Simplify (m+4)2.
Rewrite (m+4)2 as (m+4)(m+4).
25m=(m+4)(m+4)
Expand (m+4)(m+4) using the FOIL Method.
Apply the distributive property.
25m=m(m+4)+4(m+4)
Apply the distributive property.
25m=m⋅m+m⋅4+4(m+4)
Apply the distributive property.
25m=m⋅m+m⋅4+4m+4⋅4
25m=m⋅m+m⋅4+4m+4⋅4
Simplify and combine like terms.
Simplify each term.
Multiply m by m.
25m=m2+m⋅4+4m+4⋅4
Move 4 to the left of m.
25m=m2+4⋅m+4m+4⋅4
Multiply 4 by 4.
25m=m2+4m+4m+16
25m=m2+4m+4m+16
25m=m2+8m+16
25m=m2+8m+16
25m=m2+8m+16
Since m is on the right side of the equation, switch the sides so it is on the left side of the equation.
m2+8m+16=25m
Move all terms containing m to the left side of the equation.
Subtract 25m from both sides of the equation.
m2+8m+16-25m=0
Subtract 25m from 8m.
m2-17m+16=0
m2-17m+16=0
Factor m2-17m+16 using the AC method.
Consider the form x2+bx+c. Find a pair of integers whose product is c and whose sum is b. In this case, whose product is 16 and whose sum is -17.
-16,-1
Write the factored form using these integers.
(m-16)(m-1)=0
(m-16)(m-1)=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-16=0
m-1=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
m-16=0
Add 16 to both sides of the equation.
m=16
m=16
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
m-1=0
Add 1 to both sides of the equation.
m=1
m=1
The final solution is all the values that make (m-16)(m-1)=0 true.
m=16,1
m=16,1
Solve for m m+4=5 square root of m

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