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Simplifying 2y2 + -72 = 12y Reorder the terms: -72 + 2y2 = 12y Solving -72 + 2y2 = 12y Solving for variable 'y'. Reorder the terms: -72 + -12y + 2y2 = 12y + -12y Combine like terms: 12y + -12y = 0 -72 + -12y + 2y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-36 + -6y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-36 + -6y + y2)' equal to zero and attempt to solve: Simplifying -36 + -6y + y2 = 0 Solving -36 + -6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -6y + 36 + y2 = 0 + 36 Reorder the terms: -36 + 36 + -6y + y2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -6y + y2 = 0 + 36 -6y + y2 = 0 + 36 Combine like terms: 0 + 36 = 36 -6y + y2 = 36 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 = 36 + 9 Reorder the terms: 9 + -6y + y2 = 36 + 9 Combine like terms: 36 + 9 = 45 9 + -6y + y2 = 45 Factor a perfect square on the left side: (y + -3)(y + -3) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (y + -3) equal to 6.708203933 and -6.708203933.Subproblem 1
y + -3 = 6.708203933 Simplifying y + -3 = 6.708203933 Reorder the terms: -3 + y = 6.708203933 Solving -3 + y = 6.708203933 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 = 6.708203933 + 3 Combine like terms: -3 + 3 = 0 0 + y = 6.708203933 + 3 y = 6.708203933 + 3 Combine like terms: 6.708203933 + 3 = 9.708203933 y = 9.708203933 Simplifying y = 9.708203933Subproblem 2
y + -3 = -6.708203933 Simplifying y + -3 = -6.708203933 Reorder the terms: -3 + y = -6.708203933 Solving -3 + y = -6.708203933 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 = -6.708203933 + 3 Combine like terms: -3 + 3 = 0 0 + y = -6.708203933 + 3 y = -6.708203933 + 3 Combine like terms: -6.708203933 + 3 = -3.708203933 y = -3.708203933 Simplifying y = -3.708203933Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.708203933, -3.708203933}Solution
y = {9.708203933, -3.708203933}
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