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Simplifying y2 + 3y + -120 = 0 Reorder the terms: -120 + 3y + y2 = 0 Solving -120 + 3y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '120' to each side of the equation. -120 + 3y + 120 + y2 = 0 + 120 Reorder the terms: -120 + 120 + 3y + y2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 3y + y2 = 0 + 120 3y + y2 = 0 + 120 Combine like terms: 0 + 120 = 120 3y + y2 = 120 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 = 120 + 2.25 Reorder the terms: 2.25 + 3y + y2 = 120 + 2.25 Combine like terms: 120 + 2.25 = 122.25 2.25 + 3y + y2 = 122.25 Factor a perfect square on the left side: (y + 1.5)(y + 1.5) = 122.25 Calculate the square root of the right side: 11.056672194 Break this problem into two subproblems by setting (y + 1.5) equal to 11.056672194 and -11.056672194.Subproblem 1
y + 1.5 = 11.056672194 Simplifying y + 1.5 = 11.056672194 Reorder the terms: 1.5 + y = 11.056672194 Solving 1.5 + y = 11.056672194 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 = 11.056672194 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = 11.056672194 + -1.5 y = 11.056672194 + -1.5 Combine like terms: 11.056672194 + -1.5 = 9.556672194 y = 9.556672194 Simplifying y = 9.556672194Subproblem 2
y + 1.5 = -11.056672194 Simplifying y + 1.5 = -11.056672194 Reorder the terms: 1.5 + y = -11.056672194 Solving 1.5 + y = -11.056672194 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 = -11.056672194 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + y = -11.056672194 + -1.5 y = -11.056672194 + -1.5 Combine like terms: -11.056672194 + -1.5 = -12.556672194 y = -12.556672194 Simplifying y = -12.556672194Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.556672194, -12.556672194}
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