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

m-5=m-11
Move all terms not containing m to the right side of the equation.
Add 5 to both sides of the equation.
m=m-11+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
Simplify each side of the equation.
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
Solve for m.
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