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Simplifying (4 + -1y)(4 + -1y) + y2 = 16 Multiply (4 + -1y) * (4 + -1y) (4(4 + -1y) + -1y * (4 + -1y)) + y2 = 16 ((4 * 4 + -1y * 4) + -1y * (4 + -1y)) + y2 = 16 ((16 + -4y) + -1y * (4 + -1y)) + y2 = 16 (16 + -4y + (4 * -1y + -1y * -1y)) + y2 = 16 (16 + -4y + (-4y + 1y2)) + y2 = 16 Combine like terms: -4y + -4y = -8y (16 + -8y + 1y2) + y2 = 16 Combine like terms: 1y2 + y2 = 2y2 16 + -8y + 2y2 = 16 Add '-16' to each side of the equation. 16 + -8y + -16 + 2y2 = 16 + -16 Reorder the terms: 16 + -16 + -8y + 2y2 = 16 + -16 Combine like terms: 16 + -16 = 0 0 + -8y + 2y2 = 16 + -16 -8y + 2y2 = 16 + -16 Combine like terms: 16 + -16 = 0 -8y + 2y2 = 0 Solving -8y + 2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(-4 + y) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0Subproblem 2
Set the factor '(-4 + y)' equal to zero and attempt to solve: Simplifying -4 + y = 0 Solving -4 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = 0 + 4 Combine like terms: -4 + 4 = 0 0 + y = 0 + 4 y = 0 + 4 Combine like terms: 0 + 4 = 4 y = 4 Simplifying y = 4Solution
y = {0, 4}
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