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Simplifying y2 = -45 + 15y Solving y2 = -45 + 15y Solving for variable 'y'. Reorder the terms: 45 + -15y + y2 = -45 + 15y + 45 + -15y Reorder the terms: 45 + -15y + y2 = -45 + 45 + 15y + -15y Combine like terms: -45 + 45 = 0 45 + -15y + y2 = 0 + 15y + -15y 45 + -15y + y2 = 15y + -15y Combine like terms: 15y + -15y = 0 45 + -15y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + -15y + -45 + y2 = 0 + -45 Reorder the terms: 45 + -45 + -15y + y2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -15y + y2 = 0 + -45 -15y + y2 = 0 + -45 Combine like terms: 0 + -45 = -45 -15y + y2 = -45 The y term is -15y. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15y + 56.25 + y2 = -45 + 56.25 Reorder the terms: 56.25 + -15y + y2 = -45 + 56.25 Combine like terms: -45 + 56.25 = 11.25 56.25 + -15y + y2 = 11.25 Factor a perfect square on the left side: (y + -7.5)(y + -7.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (y + -7.5) equal to 3.354101966 and -3.354101966.Subproblem 1
y + -7.5 = 3.354101966 Simplifying y + -7.5 = 3.354101966 Reorder the terms: -7.5 + y = 3.354101966 Solving -7.5 + y = 3.354101966 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + y = 3.354101966 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + y = 3.354101966 + 7.5 y = 3.354101966 + 7.5 Combine like terms: 3.354101966 + 7.5 = 10.854101966 y = 10.854101966 Simplifying y = 10.854101966Subproblem 2
y + -7.5 = -3.354101966 Simplifying y + -7.5 = -3.354101966 Reorder the terms: -7.5 + y = -3.354101966 Solving -7.5 + y = -3.354101966 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + y = -3.354101966 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + y = -3.354101966 + 7.5 y = -3.354101966 + 7.5 Combine like terms: -3.354101966 + 7.5 = 4.145898034 y = 4.145898034 Simplifying y = 4.145898034Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.854101966, 4.145898034}
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