Solve for y square root of y-7 = square root of y-1

Math
y-7=y-1
To remove the radical on the left side of the equation, square both sides of the equation.
y-72=(y-1)2
Simplify each side of the equation.
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Multiply the exponents in ((y-7)12)2.
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Apply the power rule and multiply exponents, (am)n=amn.
(y-7)12⋅2=(y-1)2
Cancel the common factor of 2.
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Cancel the common factor.
(y-7)12⋅2=(y-1)2
Rewrite the expression.
(y-7)1=(y-1)2
(y-7)1=(y-1)2
(y-7)1=(y-1)2
Simplify.
y-7=(y-1)2
y-7=(y-1)2
Solve for y.
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Simplify (y-1)2.
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Rewrite (y-1)2 as (y-1)(y-1).
y-7=(y-1)(y-1)
Expand (y-1)(y-1) using the FOIL Method.
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Apply the distributive property.
y-7=y(y-1)-1(y-1)
Apply the distributive property.
y-7=yy+y⋅-1-1(y-1)
Apply the distributive property.
y-7=yy+y⋅-1-1y-1⋅-1
y-7=yy+y⋅-1-1y-1⋅-1
Simplify and combine like terms.
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Simplify each term.
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Multiply yy.
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Raise y to the power of 1.
y-7=y1y+y⋅-1-1y-1⋅-1
Raise y to the power of 1.
y-7=y1y1+y⋅-1-1y-1⋅-1
Use the power rule aman=am+n to combine exponents.
y-7=y1+1+y⋅-1-1y-1⋅-1
Add 1 and 1.
y-7=y2+y⋅-1-1y-1⋅-1
y-7=y2+y⋅-1-1y-1⋅-1
Rewrite y2 as y.
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Use axn=axn to rewrite y as y12.
y-7=(y12)2+y⋅-1-1y-1⋅-1
Apply the power rule and multiply exponents, (am)n=amn.
y-7=y12⋅2+y⋅-1-1y-1⋅-1
Combine 12 and 2.
y-7=y22+y⋅-1-1y-1⋅-1
Cancel the common factor of 2.
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Cancel the common factor.
y-7=y22+y⋅-1-1y-1⋅-1
Divide 1 by 1.
y-7=y1+y⋅-1-1y-1⋅-1
y-7=y1+y⋅-1-1y-1⋅-1
Simplify.
y-7=y+y⋅-1-1y-1⋅-1
y-7=y+y⋅-1-1y-1⋅-1
Move -1 to the left of y.
y-7=y-1⋅y-1y-1⋅-1
Rewrite -1y as -y.
y-7=y-y-1y-1⋅-1
Rewrite -1y as -y.
y-7=y-y-y-1⋅-1
Multiply -1 by -1.
y-7=y-y-y+1
y-7=y-y-y+1
Subtract y from -y.
y-7=y-2y+1
y-7=y-2y+1
y-7=y-2y+1
Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.
y-2y+1=y-7
Move all terms not containing y to the right side of the equation.
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Subtract y from both sides of the equation.
-2y+1=y-7-y
Subtract 1 from both sides of the equation.
-2y=y-7-y-1
Combine the opposite terms in y-7-y-1.
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Subtract y from y.
-2y=0-7-1
Subtract 7 from 0.
-2y=-7-1
-2y=-7-1
Subtract 1 from -7.
-2y=-8
-2y=-8
Divide each term by -2 and simplify.
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Divide each term in -2y=-8 by -2.
-2y-2=-8-2
Cancel the common factor of -2.
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Cancel the common factor.
-2y-2=-8-2
Divide y by 1.
y=-8-2
y=-8-2
Divide -8 by -2.
y=4
y=4
To remove the radical on the left side of the equation, square both sides of the equation.
y2=42
Simplify each side of the equation.
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Multiply the exponents in (y12)2.
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Apply the power rule and multiply exponents, (am)n=amn.
y12⋅2=42
Cancel the common factor of 2.
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Cancel the common factor.
y12⋅2=42
Rewrite the expression.
y1=42
y1=42
y1=42
Simplify.
y=42
Raise 4 to the power of 2.
y=16
y=16
y=16
Solve for y square root of y-7 = square root of y-1

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