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

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

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

Add 5y and 5y.

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