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Simplifying 2y2 + -12y + 8 = 0 Reorder the terms: 8 + -12y + 2y2 = 0 Solving 8 + -12y + 2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -6y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -6y + y2)' equal to zero and attempt to solve: Simplifying 4 + -6y + y2 = 0 Solving 4 + -6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -6y + -4 + y2 = 0 + -4 Reorder the terms: 4 + -4 + -6y + y2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -6y + y2 = 0 + -4 -6y + y2 = 0 + -4 Combine like terms: 0 + -4 = -4 -6y + y2 = -4 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = -4 + 9 Reorder the terms: 9 + -6y + y2 = -4 + 9 Combine like terms: -4 + 9 = 5 9 + -6y + y2 = 5 Factor a perfect square on the left side: (y + -3)(y + -3) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (y + -3) equal to 2.236067978 and -2.236067978.Subproblem 1
y + -3 = 2.236067978 Simplifying y + -3 = 2.236067978 Reorder the terms: -3 + y = 2.236067978 Solving -3 + y = 2.236067978 Solving for variable 'y'. 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 = 2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + y = 2.236067978 + 3 y = 2.236067978 + 3 Combine like terms: 2.236067978 + 3 = 5.236067978 y = 5.236067978 Simplifying y = 5.236067978Subproblem 2
y + -3 = -2.236067978 Simplifying y + -3 = -2.236067978 Reorder the terms: -3 + y = -2.236067978 Solving -3 + y = -2.236067978 Solving for variable 'y'. 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 = -2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + y = -2.236067978 + 3 y = -2.236067978 + 3 Combine like terms: -2.236067978 + 3 = 0.763932022 y = 0.763932022 Simplifying y = 0.763932022Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.236067978, 0.763932022}Solution
y = {5.236067978, 0.763932022}
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