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Simplifying (2y + -7) * 12y + -5 = -3 Reorder the terms: (-7 + 2y) * 12y + -5 = -3 Reorder the terms for easier multiplication: 12y(-7 + 2y) + -5 = -3 (-7 * 12y + 2y * 12y) + -5 = -3 (-84y + 24y2) + -5 = -3 Reorder the terms: -5 + -84y + 24y2 = -3 Solving -5 + -84y + 24y2 = -3 Solving for variable 'y'. Reorder the terms: -5 + 3 + -84y + 24y2 = -3 + 3 Combine like terms: -5 + 3 = -2 -2 + -84y + 24y2 = -3 + 3 Combine like terms: -3 + 3 = 0 -2 + -84y + 24y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + -42y + 12y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -42y + 12y2)' equal to zero and attempt to solve: Simplifying -1 + -42y + 12y2 = 0 Solving -1 + -42y + 12y2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.08333333333 + -3.5y + y2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + -3.5y + 0.08333333333 + y2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + -3.5y + y2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + -3.5y + y2 = 0 + 0.08333333333 -3.5y + y2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 -3.5y + y2 = 0.08333333333 The y term is -3.5y. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5y + 3.0625 + y2 = 0.08333333333 + 3.0625 Reorder the terms: 3.0625 + -3.5y + y2 = 0.08333333333 + 3.0625 Combine like terms: 0.08333333333 + 3.0625 = 3.14583333333 3.0625 + -3.5y + y2 = 3.14583333333 Factor a perfect square on the left side: (y + -1.75)(y + -1.75) = 3.14583333333 Calculate the square root of the right side: 1.773649721 Break this problem into two subproblems by setting (y + -1.75) equal to 1.773649721 and -1.773649721.Subproblem 1
y + -1.75 = 1.773649721 Simplifying y + -1.75 = 1.773649721 Reorder the terms: -1.75 + y = 1.773649721 Solving -1.75 + y = 1.773649721 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + y = 1.773649721 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + y = 1.773649721 + 1.75 y = 1.773649721 + 1.75 Combine like terms: 1.773649721 + 1.75 = 3.523649721 y = 3.523649721 Simplifying y = 3.523649721Subproblem 2
y + -1.75 = -1.773649721 Simplifying y + -1.75 = -1.773649721 Reorder the terms: -1.75 + y = -1.773649721 Solving -1.75 + y = -1.773649721 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + y = -1.773649721 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + y = -1.773649721 + 1.75 y = -1.773649721 + 1.75 Combine like terms: -1.773649721 + 1.75 = -0.023649721 y = -0.023649721 Simplifying y = -0.023649721Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.523649721, -0.023649721}Solution
y = {3.523649721, -0.023649721}
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