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Simplifying 2y2 + -15y + 32 + -1y2 + -4y + 4 = 0 Reorder the terms: 32 + 4 + -15y + -4y + 2y2 + -1y2 = 0 Combine like terms: 32 + 4 = 36 36 + -15y + -4y + 2y2 + -1y2 = 0 Combine like terms: -15y + -4y = -19y 36 + -19y + 2y2 + -1y2 = 0 Combine like terms: 2y2 + -1y2 = 1y2 36 + -19y + 1y2 = 0 Solving 36 + -19y + 1y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -19y + -36 + y2 = 0 + -36 Reorder the terms: 36 + -36 + -19y + y2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -19y + y2 = 0 + -36 -19y + y2 = 0 + -36 Combine like terms: 0 + -36 = -36 -19y + y2 = -36 The y term is -19y. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19y + 90.25 + y2 = -36 + 90.25 Reorder the terms: 90.25 + -19y + y2 = -36 + 90.25 Combine like terms: -36 + 90.25 = 54.25 90.25 + -19y + y2 = 54.25 Factor a perfect square on the left side: (y + -9.5)(y + -9.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (y + -9.5) equal to 7.365459931 and -7.365459931.Subproblem 1
y + -9.5 = 7.365459931 Simplifying y + -9.5 = 7.365459931 Reorder the terms: -9.5 + y = 7.365459931 Solving -9.5 + y = 7.365459931 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + y = 7.365459931 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + y = 7.365459931 + 9.5 y = 7.365459931 + 9.5 Combine like terms: 7.365459931 + 9.5 = 16.865459931 y = 16.865459931 Simplifying y = 16.865459931Subproblem 2
y + -9.5 = -7.365459931 Simplifying y + -9.5 = -7.365459931 Reorder the terms: -9.5 + y = -7.365459931 Solving -9.5 + y = -7.365459931 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + y = -7.365459931 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + y = -7.365459931 + 9.5 y = -7.365459931 + 9.5 Combine like terms: -7.365459931 + 9.5 = 2.134540069 y = 2.134540069 Simplifying y = 2.134540069Solution
The solution to the problem is based on the solutions from the subproblems. y = {16.865459931, 2.134540069}
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