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Simplifying 0.125y2 + y + -360 = 0 Reorder the terms: -360 + y + 0.125y2 = 0 Solving -360 + y + 0.125y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 0.125 the coefficient of the squared term: Divide each side by '0.125'. -2880 + 8y + y2 = 0 Move the constant term to the right: Add '2880' to each side of the equation. -2880 + 8y + 2880 + y2 = 0 + 2880 Reorder the terms: -2880 + 2880 + 8y + y2 = 0 + 2880 Combine like terms: -2880 + 2880 = 0 0 + 8y + y2 = 0 + 2880 8y + y2 = 0 + 2880 Combine like terms: 0 + 2880 = 2880 8y + y2 = 2880 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. 8y + 0.25 + y2 = 2880 + 0.25 Reorder the terms: 0.25 + 8y + y2 = 2880 + 0.25 Combine like terms: 2880 + 0.25 = 2880.25 0.25 + 8y + y2 = 2880.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = 2880.25 Calculate the square root of the right side: 53.667960647 Break this problem into two subproblems by setting (y + 0.5) equal to 53.667960647 and -53.667960647.Subproblem 1
y + 0.5 = 53.667960647 Simplifying y + 0.5 = 53.667960647 Reorder the terms: 0.5 + y = 53.667960647 Solving 0.5 + y = 53.667960647 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 = 53.667960647 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = 53.667960647 + -0.5 y = 53.667960647 + -0.5 Combine like terms: 53.667960647 + -0.5 = 53.167960647 y = 53.167960647 Simplifying y = 53.167960647Subproblem 2
y + 0.5 = -53.667960647 Simplifying y + 0.5 = -53.667960647 Reorder the terms: 0.5 + y = -53.667960647 Solving 0.5 + y = -53.667960647 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 = -53.667960647 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y = -53.667960647 + -0.5 y = -53.667960647 + -0.5 Combine like terms: -53.667960647 + -0.5 = -54.167960647 y = -54.167960647 Simplifying y = -54.167960647Solution
The solution to the problem is based on the solutions from the subproblems. y = {53.167960647, -54.167960647}
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