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Simplifying
(2y2 + 7) + (61 + -1y2) = 117
Reorder the terms:
(7 + 2y2) + (61 + -1y2) = 117
Remove parenthesis around (7 + 2y2)
7 + 2y2 + (61 + -1y2) = 117
Remove parenthesis around (61 + -1y2)
7 + 2y2 + 61 + -1y2 = 117
Reorder the terms:
7 + 61 + 2y2 + -1y2 = 117
Combine like terms: 7 + 61 = 68
68 + 2y2 + -1y2 = 117
Combine like terms: 2y2 + -1y2 = 1y2
68 + 1y2 = 117
Solving
68 + 1y2 = 117
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-68' to each side of the equation.
68 + -68 + 1y2 = 117 + -68
Combine like terms: 68 + -68 = 0
0 + 1y2 = 117 + -68
1y2 = 117 + -68
Combine like terms: 117 + -68 = 49
1y2 = 49
Divide each side by '1'.
y2 = 49
Simplifying
y2 = 49
Take the square root of each side:
y = {-7, 7}
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