# Solve for s square root of 2s+15-s=6 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
Simplify each side of the equation.
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
Solve for s.
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

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