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Simplifying (-3 + y)(-3 + y) + y * y = 9 Multiply (-3 + y) * (-3 + y) (-3(-3 + y) + y(-3 + y)) + y * y = 9 ((-3 * -3 + y * -3) + y(-3 + y)) + y * y = 9 ((9 + -3y) + y(-3 + y)) + y * y = 9 (9 + -3y + (-3 * y + y * y)) + y * y = 9 (9 + -3y + (-3y + y2)) + y * y = 9 Combine like terms: -3y + -3y = -6y (9 + -6y + y2) + y * y = 9 Multiply y * y 9 + -6y + y2 + y2 = 9 Combine like terms: y2 + y2 = 2y2 9 + -6y + 2y2 = 9 Add '-9' to each side of the equation. 9 + -6y + -9 + 2y2 = 9 + -9 Reorder the terms: 9 + -9 + -6y + 2y2 = 9 + -9 Combine like terms: 9 + -9 = 0 0 + -6y + 2y2 = 9 + -9 -6y + 2y2 = 9 + -9 Combine like terms: 9 + -9 = 0 -6y + 2y2 = 0 Solving -6y + 2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2y'. 2y(-3 + 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 '(-3 + y)' equal to zero and attempt to solve: Simplifying -3 + y = 0 Solving -3 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + y = 0 + 3 y = 0 + 3 Combine like terms: 0 + 3 = 3 y = 3 Simplifying y = 3Solution
y = {0, 3}
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