# Solve for y square root of 17*y+15=y+5

17⋅y+15=y+5
To remove the radical on the left side of the equation, square both sides of the equation.
17⋅y+152=(y+5)2
Multiply the exponents in ((17⋅y+15)12)2.
Apply the power rule and multiply exponents, (am)n=amn.
(17⋅y+15)12⋅2=(y+5)2
Cancel the common factor of 2.
Cancel the common factor.
(17⋅y+15)12⋅2=(y+5)2
Rewrite the expression.
(17⋅y+15)1=(y+5)2
(17⋅y+15)1=(y+5)2
17y+15=(y+5)2
Solve for y.
Simplify (y+5)2.
Rewrite (y+5)2 as (y+5)(y+5).
17y+15=(y+5)(y+5)
Expand (y+5)(y+5) using the FOIL Method.
Apply the distributive property.
17y+15=y(y+5)+5(y+5)
Apply the distributive property.
17y+15=y⋅y+y⋅5+5(y+5)
Apply the distributive property.
17y+15=y⋅y+y⋅5+5y+5⋅5
17y+15=y⋅y+y⋅5+5y+5⋅5
Simplify and combine like terms.
Simplify each term.
Multiply y by y.
17y+15=y2+y⋅5+5y+5⋅5
Move 5 to the left of y.
17y+15=y2+5⋅y+5y+5⋅5
Multiply 5 by 5.
17y+15=y2+5y+5y+25
17y+15=y2+5y+5y+25
17y+15=y2+10y+25
17y+15=y2+10y+25
17y+15=y2+10y+25
Since y is on the right side of the equation, switch the sides so it is on the left side of the equation.
y2+10y+25=17y+15
Move all terms containing y to the left side of the equation.
Subtract 17y from both sides of the equation.
y2+10y+25-17y=15
Subtract 17y from 10y.
y2-7y+25=15
y2-7y+25=15
Move 15 to the left side of the equation by subtracting it from both sides.
y2-7y+25-15=0
Subtract 15 from 25.
y2-7y+10=0
Factor y2-7y+10 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 10 and whose sum is -7.
-5,-2
Write the factored form using these integers.
(y-5)(y-2)=0
(y-5)(y-2)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
y-5=0
y-2=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
y-5=0
Add 5 to both sides of the equation.
y=5
y=5
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
y-2=0
Add 2 to both sides of the equation.
y=2
y=2
The final solution is all the values that make (y-5)(y-2)=0 true.
y=5,2
y=5,2
Solve for y square root of 17*y+15=y+5

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