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Simplifying 12500y2 + 3357.6y + -1284.8 = 0 Reorder the terms: -1284.8 + 3357.6y + 12500y2 = 0 Solving -1284.8 + 3357.6y + 12500y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 12500 the coefficient of the squared term: Divide each side by '12500'. -0.102784 + 0.268608y + y2 = 0 Move the constant term to the right: Add '0.102784' to each side of the equation. -0.102784 + 0.268608y + 0.102784 + y2 = 0 + 0.102784 Reorder the terms: -0.102784 + 0.102784 + 0.268608y + y2 = 0 + 0.102784 Combine like terms: -0.102784 + 0.102784 = 0.000000 0.000000 + 0.268608y + y2 = 0 + 0.102784 0.268608y + y2 = 0 + 0.102784 Combine like terms: 0 + 0.102784 = 0.102784 0.268608y + y2 = 0.102784 The y term is 0.268608y. Take half its coefficient (0.134304). Square it (0.01803756442) and add it to both sides. Add '0.01803756442' to each side of the equation. 0.268608y + 0.01803756442 + y2 = 0.102784 + 0.01803756442 Reorder the terms: 0.01803756442 + 0.268608y + y2 = 0.102784 + 0.01803756442 Combine like terms: 0.102784 + 0.01803756442 = 0.12082156442 0.01803756442 + 0.268608y + y2 = 0.12082156442 Factor a perfect square on the left side: (y + 0.134304)(y + 0.134304) = 0.12082156442 Calculate the square root of the right side: 0.347593965 Break this problem into two subproblems by setting (y + 0.134304) equal to 0.347593965 and -0.347593965.Subproblem 1
y + 0.134304 = 0.347593965 Simplifying y + 0.134304 = 0.347593965 Reorder the terms: 0.134304 + y = 0.347593965 Solving 0.134304 + y = 0.347593965 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.134304' to each side of the equation. 0.134304 + -0.134304 + y = 0.347593965 + -0.134304 Combine like terms: 0.134304 + -0.134304 = 0.000000 0.000000 + y = 0.347593965 + -0.134304 y = 0.347593965 + -0.134304 Combine like terms: 0.347593965 + -0.134304 = 0.213289965 y = 0.213289965 Simplifying y = 0.213289965Subproblem 2
y + 0.134304 = -0.347593965 Simplifying y + 0.134304 = -0.347593965 Reorder the terms: 0.134304 + y = -0.347593965 Solving 0.134304 + y = -0.347593965 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.134304' to each side of the equation. 0.134304 + -0.134304 + y = -0.347593965 + -0.134304 Combine like terms: 0.134304 + -0.134304 = 0.000000 0.000000 + y = -0.347593965 + -0.134304 y = -0.347593965 + -0.134304 Combine like terms: -0.347593965 + -0.134304 = -0.481897965 y = -0.481897965 Simplifying y = -0.481897965Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.213289965, -0.481897965}
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