y+10-10=y

Add 10 to both sides of the equation.

y+10=y+10

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

y+102=(y+10)2

Multiply the exponents in ((y+10)12)2.

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

(y+10)12⋅2=(y+10)2

Cancel the common factor of 2.

Cancel the common factor.

(y+10)12⋅2=(y+10)2

Rewrite the expression.

(y+10)1=(y+10)2

(y+10)1=(y+10)2

(y+10)1=(y+10)2

Simplify.

y+10=(y+10)2

y+10=(y+10)2

Simplify (y+10)2.

Rewrite (y+10)2 as (y+10)(y+10).

y+10=(y+10)(y+10)

Expand (y+10)(y+10) using the FOIL Method.

Apply the distributive property.

y+10=y(y+10)+10(y+10)

Apply the distributive property.

y+10=y⋅y+y⋅10+10(y+10)

Apply the distributive property.

y+10=y⋅y+y⋅10+10y+10⋅10

y+10=y⋅y+y⋅10+10y+10⋅10

Simplify and combine like terms.

Simplify each term.

Multiply y by y.

y+10=y2+y⋅10+10y+10⋅10

Move 10 to the left of y.

y+10=y2+10⋅y+10y+10⋅10

Multiply 10 by 10.

y+10=y2+10y+10y+100

y+10=y2+10y+10y+100

Add 10y and 10y.

y+10=y2+20y+100

y+10=y2+20y+100

y+10=y2+20y+100

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

y2+20y+100=y+10

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

Subtract y from both sides of the equation.

y2+20y+100-y=10

Subtract y from 20y.

y2+19y+100=10

y2+19y+100=10

Move 10 to the left side of the equation by subtracting it from both sides.

y2+19y+100-10=0

Subtract 10 from 100.

y2+19y+90=0

Factor y2+19y+90 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 90 and whose sum is 19.

9,10

Write the factored form using these integers.

(y+9)(y+10)=0

(y+9)(y+10)=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+9=0

y+10=0

Set the first factor equal to 0 and solve.

Set the first factor equal to 0.

y+9=0

Subtract 9 from both sides of the equation.

y=-9

y=-9

Set the next factor equal to 0 and solve.

Set the next factor equal to 0.

y+10=0

Subtract 10 from both sides of the equation.

y=-10

y=-10

The final solution is all the values that make (y+9)(y+10)=0 true.

y=-9,-10

y=-9,-10

Solve for y square root of y+10-10=y