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

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

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

Add 4m and 4m.

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