2s+15-s=6

Add s to both sides of the equation.

2s+15=6+s

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

2s+152=(6+s)2

Multiply the exponents in ((2s+15)12)2.

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

(2s+15)12⋅2=(6+s)2

Cancel the common factor of 2.

Cancel the common factor.

(2s+15)12⋅2=(6+s)2

Rewrite the expression.

(2s+15)1=(6+s)2

(2s+15)1=(6+s)2

(2s+15)1=(6+s)2

Simplify.

2s+15=(6+s)2

2s+15=(6+s)2

Simplify (6+s)2.

Rewrite (6+s)2 as (6+s)(6+s).

2s+15=(6+s)(6+s)

Expand (6+s)(6+s) using the FOIL Method.

Apply the distributive property.

2s+15=6(6+s)+s(6+s)

Apply the distributive property.

2s+15=6⋅6+6s+s(6+s)

Apply the distributive property.

2s+15=6⋅6+6s+s⋅6+s⋅s

2s+15=6⋅6+6s+s⋅6+s⋅s

Simplify and combine like terms.

Simplify each term.

Multiply 6 by 6.

2s+15=36+6s+s⋅6+s⋅s

Move 6 to the left of s.

2s+15=36+6s+6⋅s+s⋅s

Multiply s by s.

2s+15=36+6s+6s+s2

2s+15=36+6s+6s+s2

Add 6s and 6s.

2s+15=36+12s+s2

2s+15=36+12s+s2

2s+15=36+12s+s2

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

36+12s+s2=2s+15

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

Subtract 2s from both sides of the equation.

36+12s+s2-2s=15

Subtract 2s from 12s.

36+s2+10s=15

36+s2+10s=15

Move 15 to the left side of the equation by subtracting it from both sides.

36+s2+10s-15=0

Subtract 15 from 36.

s2+10s+21=0

Factor s2+10s+21 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 21 and whose sum is 10.

3,7

Write the factored form using these integers.

(s+3)(s+7)=0

(s+3)(s+7)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

s+3=0

s+7=0

Set the first factor equal to 0 and solve.

Set the first factor equal to 0.

s+3=0

Subtract 3 from both sides of the equation.

s=-3

s=-3

Set the next factor equal to 0 and solve.

Set the next factor equal to 0.

s+7=0

Subtract 7 from both sides of the equation.

s=-7

s=-7

The final solution is all the values that make (s+3)(s+7)=0 true.

s=-3,-7

s=-3,-7

Exclude the solutions that do not make 2s+15-s=6 true.

s=-3

Solve for s square root of 2s+15-s=6