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Simplifying 2y2 = -12y + 24 Reorder the terms: 2y2 = 24 + -12y Solving 2y2 = 24 + -12y Solving for variable 'y'. Reorder the terms: -24 + 12y + 2y2 = 24 + -12y + -24 + 12y Reorder the terms: -24 + 12y + 2y2 = 24 + -24 + -12y + 12y Combine like terms: 24 + -24 = 0 -24 + 12y + 2y2 = 0 + -12y + 12y -24 + 12y + 2y2 = -12y + 12y Combine like terms: -12y + 12y = 0 -24 + 12y + 2y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 6y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + 6y + y2)' equal to zero and attempt to solve: Simplifying -12 + 6y + y2 = 0 Solving -12 + 6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 6y + 12 + y2 = 0 + 12 Reorder the terms: -12 + 12 + 6y + y2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 6y + y2 = 0 + 12 6y + y2 = 0 + 12 Combine like terms: 0 + 12 = 12 6y + y2 = 12 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 = 12 + 9 Reorder the terms: 9 + 6y + y2 = 12 + 9 Combine like terms: 12 + 9 = 21 9 + 6y + y2 = 21 Factor a perfect square on the left side: (y + 3)(y + 3) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (y + 3) equal to 4.582575695 and -4.582575695.Subproblem 1
y + 3 = 4.582575695 Simplifying y + 3 = 4.582575695 Reorder the terms: 3 + y = 4.582575695 Solving 3 + y = 4.582575695 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 = 4.582575695 + -3 Combine like terms: 3 + -3 = 0 0 + y = 4.582575695 + -3 y = 4.582575695 + -3 Combine like terms: 4.582575695 + -3 = 1.582575695 y = 1.582575695 Simplifying y = 1.582575695Subproblem 2
y + 3 = -4.582575695 Simplifying y + 3 = -4.582575695 Reorder the terms: 3 + y = -4.582575695 Solving 3 + y = -4.582575695 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 = -4.582575695 + -3 Combine like terms: 3 + -3 = 0 0 + y = -4.582575695 + -3 y = -4.582575695 + -3 Combine like terms: -4.582575695 + -3 = -7.582575695 y = -7.582575695 Simplifying y = -7.582575695Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.582575695, -7.582575695}Solution
y = {1.582575695, -7.582575695}
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