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Simplifying 36y2 + y + -44 = 0 Reorder the terms: -44 + y + 36y2 = 0 Solving -44 + y + 36y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -1.222222222 + 0.02777777778y + y2 = 0 Move the constant term to the right: Add '1.222222222' to each side of the equation. -1.222222222 + 0.02777777778y + 1.222222222 + y2 = 0 + 1.222222222 Reorder the terms: -1.222222222 + 1.222222222 + 0.02777777778y + y2 = 0 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + 0.02777777778y + y2 = 0 + 1.222222222 0.02777777778y + y2 = 0 + 1.222222222 Combine like terms: 0 + 1.222222222 = 1.222222222 0.02777777778y + y2 = 1.222222222 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.02777777778y + 0.25 + y2 = 1.222222222 + 0.25 Reorder the terms: 0.25 + 0.02777777778y + y2 = 1.222222222 + 0.25 Combine like terms: 1.222222222 + 0.25 = 1.472222222 0.25 + 0.02777777778y + y2 = 1.472222222 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 1.472222222 Calculate the square root of the right side: 1.213351648 Break this problem into two subproblems by setting (y + 0.5) equal to 1.213351648 and -1.213351648.Subproblem 1
y + 0.5 = 1.213351648 Simplifying y + 0.5 = 1.213351648 Reorder the terms: 0.5 + y = 1.213351648 Solving 0.5 + y = 1.213351648 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = 1.213351648 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 1.213351648 + -0.5 y = 1.213351648 + -0.5 Combine like terms: 1.213351648 + -0.5 = 0.713351648 y = 0.713351648 Simplifying y = 0.713351648Subproblem 2
y + 0.5 = -1.213351648 Simplifying y + 0.5 = -1.213351648 Reorder the terms: 0.5 + y = -1.213351648 Solving 0.5 + y = -1.213351648 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + y = -1.213351648 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -1.213351648 + -0.5 y = -1.213351648 + -0.5 Combine like terms: -1.213351648 + -0.5 = -1.713351648 y = -1.713351648 Simplifying y = -1.713351648Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.713351648, -1.713351648}
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