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Simplifying 12y2 + -36y + -6 = 0 Reorder the terms: -6 + -36y + 12y2 = 0 Solving -6 + -36y + 12y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '6'. 6(-1 + -6y + 2y2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-1 + -6y + 2y2)' equal to zero and attempt to solve: Simplifying -1 + -6y + 2y2 = 0 Solving -1 + -6y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -3y + y2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -3y + 0.5 + y2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -3y + y2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -3y + y2 = 0 + 0.5 -3y + y2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -3y + y2 = 0.5 The y term is -3y. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3y + 2.25 + y2 = 0.5 + 2.25 Reorder the terms: 2.25 + -3y + y2 = 0.5 + 2.25 Combine like terms: 0.5 + 2.25 = 2.75 2.25 + -3y + y2 = 2.75 Factor a perfect square on the left side: (y + -1.5)(y + -1.5) = 2.75 Calculate the square root of the right side: 1.658312395 Break this problem into two subproblems by setting (y + -1.5) equal to 1.658312395 and -1.658312395.Subproblem 1
y + -1.5 = 1.658312395 Simplifying y + -1.5 = 1.658312395 Reorder the terms: -1.5 + y = 1.658312395 Solving -1.5 + y = 1.658312395 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = 1.658312395 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 1.658312395 + 1.5 y = 1.658312395 + 1.5 Combine like terms: 1.658312395 + 1.5 = 3.158312395 y = 3.158312395 Simplifying y = 3.158312395Subproblem 2
y + -1.5 = -1.658312395 Simplifying y + -1.5 = -1.658312395 Reorder the terms: -1.5 + y = -1.658312395 Solving -1.5 + y = -1.658312395 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = -1.658312395 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -1.658312395 + 1.5 y = -1.658312395 + 1.5 Combine like terms: -1.658312395 + 1.5 = -0.158312395 y = -0.158312395 Simplifying y = -0.158312395Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.158312395, -0.158312395}Solution
y = {3.158312395, -0.158312395}
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