Solve. (Be sure to check your solution):?

Question

Solve.
sqrt(48 - 2y) = y

Answer 1

squaring both sides
48-2y=y^2
=>y^2+2y-48=0
=>(y+8)(y-6)=0
=>y=-8 or +6
sub y=-8
rt of 64=-8 checks
suby=+6
rt of 36=6 checks

Answer 2

sqrt(48 - 2y) = y

Your first step would be to square both sides, effectively eliminating the square root.

48 - 2y = y^2

Now, bring everything over to one side.

0 = y^2 + 2y - 48

And then we factor

(y - 6)(y + 8) = 0

Yielding the results y = -8 and y = 6

BUT WAIT! We can't assume both values work, because sometimes squaring both sides of an equation adds solutions. As an example, take this one:

x = 1

Square both sides, and you get

x^2 = 1

If we were to solve that, we'd then get:

x^2 - 1 = 0, yielding (x-1)(x+1) = 0, so x = 1 and x = -1.
As you can see, we started at x = 1 and ended up with two solutions. For that reason, we definitely have to check our solutions.

Test y = 6:
sqrt (48 - 2(6)) = 6?
sqrt(48 - 12) = 6?
sqrt(36) = 6?
This is true, for y = 6 checks out.

Test y = -8
sqrt(48 - 2(-8)) = -8?
sqrt(48 + 16) = -8?
sqrt(64) = -8?
This is false, because sqrt(64) means the "positive" square root. y = -8 fails.

Therefore, y = 6

Answer 3

Sqrt(48 - 2y) = y

Square both side,
48-2y = y^2

Arrange to general form,
y^2+2y-48=0

Factorise,
(y+8)(y-6)=0

y+8=0 or y-6=0
y= -8 or y=6

Answer 4

y^2 + 2y - 48 = 0
(y-6) (y+8) = 0
y = 6 or -8

Answer 5

y= 6

Answer 6

Square both sides.
48-2y = y squared

Isolate a term

48 = y squared + 2Y

Um, y is 6 :)

Answer 7

sqrt(48-2y)=y / ^2
48-2y=y^2
y^2+2y-48=0
y1,2=(-2+/-sqrt(4-4*(-48))/2=-1 +/- 7
y1=6
y2=-8 false answer (y=>0 because sqrt(anything)>=0)
check:
sqrt(48-2*6)=6
sqrt(36)=6 true

Answer 8

(48 - 2y)^¹/2 = y
(48 - 2y) = y²
y² + 2y - 48 = 0
(y-6)(y+8) = 0

y' = -8
y'' = 6

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