5a-11=a+6

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

5a-112=a+62

Multiply the exponents in ((5a-11)12)2.

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

(5a-11)12⋅2=a+62

Cancel the common factor of 2.

Cancel the common factor.

(5a-11)12⋅2=a+62

Rewrite the expression.

(5a-11)1=a+62

(5a-11)1=a+62

(5a-11)1=a+62

Simplify.

5a-11=a+62

Rewrite a+62 as a+6.

Use axn=axn to rewrite a+6 as (a+6)12.

5a-11=((a+6)12)2

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

5a-11=(a+6)12⋅2

Combine 12 and 2.

5a-11=(a+6)22

Cancel the common factor of 2.

Cancel the common factor.

5a-11=(a+6)22

Divide 1 by 1.

5a-11=(a+6)1

5a-11=(a+6)1

Simplify.

5a-11=a+6

5a-11=a+6

5a-11=a+6

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

Subtract a from both sides of the equation.

5a-11-a=6

Subtract a from 5a.

4a-11=6

4a-11=6

Move all terms not containing a to the right side of the equation.

Add 11 to both sides of the equation.

4a=6+11

Add 6 and 11.

4a=17

4a=17

Divide each term by 4 and simplify.

Divide each term in 4a=17 by 4.

4a4=174

Cancel the common factor of 4.

Cancel the common factor.

4a4=174

Divide a by 1.

a=174

a=174

a=174

a=174

The result can be shown in multiple forms.

Exact Form:

a=174

Decimal Form:

a=4.25

Mixed Number Form:

a=414

Solve for a square root of 5a-11 = square root of a+6