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Simplifying 0 = 5.5 * 2700 + -2733.5y + -1y2 Multiply 5.5 * 2700 0 = 14850 + -2733.5y + -1y2 Solving 0 = 14850 + -2733.5y + -1y2 Solving for variable 'y'. Combine like terms: 0 + -14850 = -14850 -14850 + 2733.5y + y2 = 14850 + -2733.5y + -1y2 + -14850 + 2733.5y + y2 Reorder the terms: -14850 + 2733.5y + y2 = 14850 + -14850 + -2733.5y + 2733.5y + -1y2 + y2 Combine like terms: 14850 + -14850 = 0 -14850 + 2733.5y + y2 = 0 + -2733.5y + 2733.5y + -1y2 + y2 -14850 + 2733.5y + y2 = -2733.5y + 2733.5y + -1y2 + y2 Combine like terms: -2733.5y + 2733.5y = 0.0 -14850 + 2733.5y + y2 = 0.0 + -1y2 + y2 -14850 + 2733.5y + y2 = -1y2 + y2 Combine like terms: -1y2 + y2 = 0 -14850 + 2733.5y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '14850' to each side of the equation. -14850 + 2733.5y + 14850 + y2 = 0 + 14850 Reorder the terms: -14850 + 14850 + 2733.5y + y2 = 0 + 14850 Combine like terms: -14850 + 14850 = 0 0 + 2733.5y + y2 = 0 + 14850 2733.5y + y2 = 0 + 14850 Combine like terms: 0 + 14850 = 14850 2733.5y + y2 = 14850 The y term is 2733.5y. Take half its coefficient (1366.75). Square it (1868005.563) and add it to both sides. Add '1868005.563' to each side of the equation. 2733.5y + 1868005.563 + y2 = 14850 + 1868005.563 Reorder the terms: 1868005.563 + 2733.5y + y2 = 14850 + 1868005.563 Combine like terms: 14850 + 1868005.563 = 1882855.563 1868005.563 + 2733.5y + y2 = 1882855.563 Factor a perfect square on the left side: (y + 1366.75)(y + 1366.75) = 1882855.563 Calculate the square root of the right side: 1372.171841644 Break this problem into two subproblems by setting (y + 1366.75) equal to 1372.171841644 and -1372.171841644.Subproblem 1
y + 1366.75 = 1372.171841644 Simplifying y + 1366.75 = 1372.171841644 Reorder the terms: 1366.75 + y = 1372.171841644 Solving 1366.75 + y = 1372.171841644 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1366.75' to each side of the equation. 1366.75 + -1366.75 + y = 1372.171841644 + -1366.75 Combine like terms: 1366.75 + -1366.75 = 0.00 0.00 + y = 1372.171841644 + -1366.75 y = 1372.171841644 + -1366.75 Combine like terms: 1372.171841644 + -1366.75 = 5.421841644 y = 5.421841644 Simplifying y = 5.421841644Subproblem 2
y + 1366.75 = -1372.171841644 Simplifying y + 1366.75 = -1372.171841644 Reorder the terms: 1366.75 + y = -1372.171841644 Solving 1366.75 + y = -1372.171841644 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1366.75' to each side of the equation. 1366.75 + -1366.75 + y = -1372.171841644 + -1366.75 Combine like terms: 1366.75 + -1366.75 = 0.00 0.00 + y = -1372.171841644 + -1366.75 y = -1372.171841644 + -1366.75 Combine like terms: -1372.171841644 + -1366.75 = -2738.921841644 y = -2738.921841644 Simplifying y = -2738.921841644Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.421841644, -2738.921841644}
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