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Simplifying 28y2 + 43y + -480 = 0 Reorder the terms: -480 + 43y + 28y2 = 0 Solving -480 + 43y + 28y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -17.14285714 + 1.535714286y + y2 = 0 Move the constant term to the right: Add '17.14285714' to each side of the equation. -17.14285714 + 1.535714286y + 17.14285714 + y2 = 0 + 17.14285714 Reorder the terms: -17.14285714 + 17.14285714 + 1.535714286y + y2 = 0 + 17.14285714 Combine like terms: -17.14285714 + 17.14285714 = 0.00000000 0.00000000 + 1.535714286y + y2 = 0 + 17.14285714 1.535714286y + y2 = 0 + 17.14285714 Combine like terms: 0 + 17.14285714 = 17.14285714 1.535714286y + y2 = 17.14285714 The y term is 1.535714286y. Take half its coefficient (0.767857143). Square it (0.5896045921) and add it to both sides. Add '0.5896045921' to each side of the equation. 1.535714286y + 0.5896045921 + y2 = 17.14285714 + 0.5896045921 Reorder the terms: 0.5896045921 + 1.535714286y + y2 = 17.14285714 + 0.5896045921 Combine like terms: 17.14285714 + 0.5896045921 = 17.7324617321 0.5896045921 + 1.535714286y + y2 = 17.7324617321 Factor a perfect square on the left side: (y + 0.767857143)(y + 0.767857143) = 17.7324617321 Calculate the square root of the right side: 4.210992963 Break this problem into two subproblems by setting (y + 0.767857143) equal to 4.210992963 and -4.210992963.Subproblem 1
y + 0.767857143 = 4.210992963 Simplifying y + 0.767857143 = 4.210992963 Reorder the terms: 0.767857143 + y = 4.210992963 Solving 0.767857143 + y = 4.210992963 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.767857143' to each side of the equation. 0.767857143 + -0.767857143 + y = 4.210992963 + -0.767857143 Combine like terms: 0.767857143 + -0.767857143 = 0.000000000 0.000000000 + y = 4.210992963 + -0.767857143 y = 4.210992963 + -0.767857143 Combine like terms: 4.210992963 + -0.767857143 = 3.44313582 y = 3.44313582 Simplifying y = 3.44313582Subproblem 2
y + 0.767857143 = -4.210992963 Simplifying y + 0.767857143 = -4.210992963 Reorder the terms: 0.767857143 + y = -4.210992963 Solving 0.767857143 + y = -4.210992963 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.767857143' to each side of the equation. 0.767857143 + -0.767857143 + y = -4.210992963 + -0.767857143 Combine like terms: 0.767857143 + -0.767857143 = 0.000000000 0.000000000 + y = -4.210992963 + -0.767857143 y = -4.210992963 + -0.767857143 Combine like terms: -4.210992963 + -0.767857143 = -4.978850106 y = -4.978850106 Simplifying y = -4.978850106Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.44313582, -4.978850106}
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