# Solve for y (y-2)^2+48=0

(y-2)2+48=0
Subtract 48 from both sides of the equation.
(y-2)2=-48
Take the square root of each side of the equation to set up the solution for y
(y-2)2⋅12=±-48
Remove the perfect root factor y-2 under the radical to solve for y.
y-2=±-48
Simplify the right side of the equation.
Rewrite -48 as -1(48).
y-2=±-1⋅48
Rewrite -1(48) as -1⋅48.
y-2=±-1⋅48
Rewrite -1 as i.
y-2=±i⋅48
Rewrite 48 as 42⋅3.
Factor 16 out of 48.
y-2=±i⋅16(3)
Rewrite 16 as 42.
y-2=±i⋅42⋅3
y-2=±i⋅42⋅3
Pull terms out from under the radical.
y-2=±i⋅(43)
Move 4 to the left of i.
y-2=±4i3
y-2=±4i3
The complete solution is the result of both the positive and negative portions of the solution.
First, use the positive value of the ± to find the first solution.
y-2=4i3
Add 2 to both sides of the equation.
y=4i3+2
Next, use the negative value of the ± to find the second solution.
y-2=-4i3
Add 2 to both sides of the equation.
y=-4i3+2
The complete solution is the result of both the positive and negative portions of the solution.
y=4i3+2,-4i3+2
y=4i3+2,-4i3+2
Solve for y (y-2)^2+48=0

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