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Simplifying (y2 + 2) + -4(8 + y) = 47 Reorder the terms: (2 + y2) + -4(8 + y) = 47 Remove parenthesis around (2 + y2) 2 + y2 + -4(8 + y) = 47 2 + y2 + (8 * -4 + y * -4) = 47 2 + y2 + (-32 + -4y) = 47 Reorder the terms: 2 + -32 + -4y + y2 = 47 Combine like terms: 2 + -32 = -30 -30 + -4y + y2 = 47 Solving -30 + -4y + y2 = 47 Solving for variable 'y'. Reorder the terms: -30 + -47 + -4y + y2 = 47 + -47 Combine like terms: -30 + -47 = -77 -77 + -4y + y2 = 47 + -47 Combine like terms: 47 + -47 = 0 -77 + -4y + y2 = 0 Factor a trinomial. (-7 + -1y)(11 + -1y) = 0Subproblem 1
Set the factor '(-7 + -1y)' equal to zero and attempt to solve: Simplifying -7 + -1y = 0 Solving -7 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1y = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1y = 0 + 7 -1y = 0 + 7 Combine like terms: 0 + 7 = 7 -1y = 7 Divide each side by '-1'. y = -7 Simplifying y = -7Subproblem 2
Set the factor '(11 + -1y)' equal to zero and attempt to solve: Simplifying 11 + -1y = 0 Solving 11 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1y = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1y = 0 + -11 -1y = 0 + -11 Combine like terms: 0 + -11 = -11 -1y = -11 Divide each side by '-1'. y = 11 Simplifying y = 11Solution
y = {-7, 11}
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