4a+9=-a+1

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

4a+92=(-a+1)2

Multiply the exponents in ((4a+9)12)2.

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

(4a+9)12⋅2=(-a+1)2

Cancel the common factor of 2.

Cancel the common factor.

(4a+9)12⋅2=(-a+1)2

Rewrite the expression.

(4a+9)1=(-a+1)2

(4a+9)1=(-a+1)2

(4a+9)1=(-a+1)2

Simplify.

4a+9=(-a+1)2

Apply the product rule to -a+1.

4a+9=(-1)2a+12

Raise -1 to the power of 2.

4a+9=1a+12

Multiply a+12 by 1.

4a+9=a+12

Rewrite a+12 as a+1.

Use axn=axn to rewrite a+1 as (a+1)12.

4a+9=((a+1)12)2

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

4a+9=(a+1)12⋅2

Combine 12 and 2.

4a+9=(a+1)22

Cancel the common factor of 2.

Cancel the common factor.

4a+9=(a+1)22

Divide 1 by 1.

4a+9=(a+1)1

4a+9=(a+1)1

Simplify.

4a+9=a+1

4a+9=a+1

4a+9=a+1

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

Subtract a from both sides of the equation.

4a+9-a=1

Subtract a from 4a.

3a+9=1

3a+9=1

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

Subtract 9 from both sides of the equation.

3a=1-9

Subtract 9 from 1.

3a=-8

3a=-8

Divide each term by 3 and simplify.

Divide each term in 3a=-8 by 3.

3a3=-83

Cancel the common factor of 3.

Cancel the common factor.

3a3=-83

Divide a by 1.

a=-83

a=-83

Move the negative in front of the fraction.

a=-83

a=-83

a=-83

Exclude the solutions that do not make 4a+9=-a+1 true.

No solution

Solve for a square root of 4a+9=- square root of a+1