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Simplifying 2y2 + -24y + -8 = 0 Reorder the terms: -8 + -24y + 2y2 = 0 Solving -8 + -24y + 2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -12y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + -12y + y2)' equal to zero and attempt to solve: Simplifying -4 + -12y + y2 = 0 Solving -4 + -12y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -12y + 4 + y2 = 0 + 4 Reorder the terms: -4 + 4 + -12y + y2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -12y + y2 = 0 + 4 -12y + y2 = 0 + 4 Combine like terms: 0 + 4 = 4 -12y + y2 = 4 The y term is -12y. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12y + 36 + y2 = 4 + 36 Reorder the terms: 36 + -12y + y2 = 4 + 36 Combine like terms: 4 + 36 = 40 36 + -12y + y2 = 40 Factor a perfect square on the left side: (y + -6)(y + -6) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (y + -6) equal to 6.32455532 and -6.32455532.Subproblem 1
y + -6 = 6.32455532 Simplifying y + -6 = 6.32455532 Reorder the terms: -6 + y = 6.32455532 Solving -6 + y = 6.32455532 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = 6.32455532 + 6 Combine like terms: -6 + 6 = 0 0 + y = 6.32455532 + 6 y = 6.32455532 + 6 Combine like terms: 6.32455532 + 6 = 12.32455532 y = 12.32455532 Simplifying y = 12.32455532Subproblem 2
y + -6 = -6.32455532 Simplifying y + -6 = -6.32455532 Reorder the terms: -6 + y = -6.32455532 Solving -6 + y = -6.32455532 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = -6.32455532 + 6 Combine like terms: -6 + 6 = 0 0 + y = -6.32455532 + 6 y = -6.32455532 + 6 Combine like terms: -6.32455532 + 6 = -0.32455532 y = -0.32455532 Simplifying y = -0.32455532Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.32455532, -0.32455532}Solution
y = {12.32455532, -0.32455532}
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