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

Math
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
Simplify each side of the equation.
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Multiply the exponents in ((y+10)12)2.
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Apply the power rule and multiply exponents, (am)n=amn.
(y+10)12⋅2=(y+10)2
Cancel the common factor of 2.
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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
Solve for y.
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Simplify (y+10)2.
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Rewrite (y+10)2 as (y+10)(y+10).
y+10=(y+10)(y+10)
Expand (y+10)(y+10) using the FOIL Method.
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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.
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Simplify each term.
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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.
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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.
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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.
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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.
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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

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