m-5=m-11

Add 5 to both sides of the equation.

m=m-11+5

Add -11 and 5.

m=m-6

m=m-6

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

m2=(m-6)2

Multiply the exponents in (m12)2.

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

m12⋅2=(m-6)2

Cancel the common factor of 2.

Cancel the common factor.

m12⋅2=(m-6)2

Rewrite the expression.

m1=(m-6)2

m1=(m-6)2

m1=(m-6)2

Simplify.

m=(m-6)2

m=(m-6)2

Simplify (m-6)2.

Rewrite (m-6)2 as (m-6)(m-6).

m=(m-6)(m-6)

Expand (m-6)(m-6) using the FOIL Method.

Apply the distributive property.

m=m(m-6)-6(m-6)

Apply the distributive property.

m=m⋅m+m⋅-6-6(m-6)

Apply the distributive property.

m=m⋅m+m⋅-6-6m-6⋅-6

m=m⋅m+m⋅-6-6m-6⋅-6

Simplify and combine like terms.

Simplify each term.

Multiply m by m.

m=m2+m⋅-6-6m-6⋅-6

Move -6 to the left of m.

m=m2-6⋅m-6m-6⋅-6

Multiply -6 by -6.

m=m2-6m-6m+36

m=m2-6m-6m+36

Subtract 6m from -6m.

m=m2-12m+36

m=m2-12m+36

m=m2-12m+36

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

m2-12m+36=m

Move all terms containing m to the left side of the equation.

Subtract m from both sides of the equation.

m2-12m+36-m=0

Subtract m from -12m.

m2-13m+36=0

m2-13m+36=0

Factor m2-13m+36 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 36 and whose sum is -13.

-9,-4

Write the factored form using these integers.

(m-9)(m-4)=0

(m-9)(m-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-9=0

m-4=0

Set the first factor equal to 0 and solve.

Set the first factor equal to 0.

m-9=0

Add 9 to both sides of the equation.

m=9

m=9

Set the next factor equal to 0 and solve.

Set the next factor equal to 0.

m-4=0

Add 4 to both sides of the equation.

m=4

m=4

The final solution is all the values that make (m-9)(m-4)=0 true.

m=9,4

m=9,4

Exclude the solutions that do not make m-5=m-11 true.

m=9

Solve using the Square Root Property square root of m-5=m-11