Question 48099
2y+7 (square root sigh) + 4 = y 
{{{(sqrt(2y+7)) + 4 = y))}}}
{{{(sqrt(2y+7)) + 4 - 4= y - 4))}}}
{{{(sqrt(2y+7)) = y - 4))}}}
{{{(sqrt(2y+7)^2) = (y - 4)^2))}}}
(2y+7) = (y - 4)(y - 4)
2y + 7 = y^2 -8y + 16
2y-2y + 7 = y^2 - 10y + 16
7 = y^2 - 10y + 16
7 -7 = y^2 - 10y + 16 - 7
0 = y^2 - 10y + 9 [Factor]
0 = (y - 9)(y - 1) [Set each factor equal to zero and solve for x]
y - 9 = 0
y = 9
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y - 1 = 0
y = 1

.
y = 9 or y = 1 [Final answer]
.
Check by plugging either answer back into the original equation.