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Simplifying y2 + -5y + -24 = 24 Reorder the terms: -24 + -5y + y2 = 24 Solving -24 + -5y + y2 = 24 Solving for variable 'y'. Reorder the terms: -24 + -24 + -5y + y2 = 24 + -24 Combine like terms: -24 + -24 = -48 -48 + -5y + y2 = 24 + -24 Combine like terms: 24 + -24 = 0 -48 + -5y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -5y + 48 + y2 = 0 + 48 Reorder the terms: -48 + 48 + -5y + y2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -5y + y2 = 0 + 48 -5y + y2 = 0 + 48 Combine like terms: 0 + 48 = 48 -5y + y2 = 48 The y term is -5y. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5y + 6.25 + y2 = 48 + 6.25 Reorder the terms: 6.25 + -5y + y2 = 48 + 6.25 Combine like terms: 48 + 6.25 = 54.25 6.25 + -5y + y2 = 54.25 Factor a perfect square on the left side: (y + -2.5)(y + -2.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (y + -2.5) equal to 7.365459931 and -7.365459931.Subproblem 1
y + -2.5 = 7.365459931 Simplifying y + -2.5 = 7.365459931 Reorder the terms: -2.5 + y = 7.365459931 Solving -2.5 + y = 7.365459931 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = 7.365459931 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = 7.365459931 + 2.5 y = 7.365459931 + 2.5 Combine like terms: 7.365459931 + 2.5 = 9.865459931 y = 9.865459931 Simplifying y = 9.865459931Subproblem 2
y + -2.5 = -7.365459931 Simplifying y + -2.5 = -7.365459931 Reorder the terms: -2.5 + y = -7.365459931 Solving -2.5 + y = -7.365459931 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = -7.365459931 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = -7.365459931 + 2.5 y = -7.365459931 + 2.5 Combine like terms: -7.365459931 + 2.5 = -4.865459931 y = -4.865459931 Simplifying y = -4.865459931Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.865459931, -4.865459931}
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