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Simplifying 5300 = (90 + -1y)(13y) Remove parenthesis around (13y) 5300 = (90 + -1y) * 13y Reorder the terms for easier multiplication: 5300 = 13y(90 + -1y) 5300 = (90 * 13y + -1y * 13y) 5300 = (1170y + -13y2) Solving 5300 = 1170y + -13y2 Solving for variable 'y'. Reorder the terms: 5300 + -1170y + 13y2 = 1170y + -1170y + -13y2 + 13y2 Combine like terms: 1170y + -1170y = 0 5300 + -1170y + 13y2 = 0 + -13y2 + 13y2 5300 + -1170y + 13y2 = -13y2 + 13y2 Combine like terms: -13y2 + 13y2 = 0 5300 + -1170y + 13y2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 407.6923077 + -90y + y2 = 0 Move the constant term to the right: Add '-407.6923077' to each side of the equation. 407.6923077 + -90y + -407.6923077 + y2 = 0 + -407.6923077 Reorder the terms: 407.6923077 + -407.6923077 + -90y + y2 = 0 + -407.6923077 Combine like terms: 407.6923077 + -407.6923077 = 0.0000000 0.0000000 + -90y + y2 = 0 + -407.6923077 -90y + y2 = 0 + -407.6923077 Combine like terms: 0 + -407.6923077 = -407.6923077 -90y + y2 = -407.6923077 The y term is -90y. Take half its coefficient (-45). Square it (2025) and add it to both sides. Add '2025' to each side of the equation. -90y + 2025 + y2 = -407.6923077 + 2025 Reorder the terms: 2025 + -90y + y2 = -407.6923077 + 2025 Combine like terms: -407.6923077 + 2025 = 1617.3076923 2025 + -90y + y2 = 1617.3076923 Factor a perfect square on the left side: (y + -45)(y + -45) = 1617.3076923 Calculate the square root of the right side: 40.215764226 Break this problem into two subproblems by setting (y + -45) equal to 40.215764226 and -40.215764226.Subproblem 1
y + -45 = 40.215764226 Simplifying y + -45 = 40.215764226 Reorder the terms: -45 + y = 40.215764226 Solving -45 + y = 40.215764226 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + y = 40.215764226 + 45 Combine like terms: -45 + 45 = 0 0 + y = 40.215764226 + 45 y = 40.215764226 + 45 Combine like terms: 40.215764226 + 45 = 85.215764226 y = 85.215764226 Simplifying y = 85.215764226Subproblem 2
y + -45 = -40.215764226 Simplifying y + -45 = -40.215764226 Reorder the terms: -45 + y = -40.215764226 Solving -45 + y = -40.215764226 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + y = -40.215764226 + 45 Combine like terms: -45 + 45 = 0 0 + y = -40.215764226 + 45 y = -40.215764226 + 45 Combine like terms: -40.215764226 + 45 = 4.784235774 y = 4.784235774 Simplifying y = 4.784235774Solution
The solution to the problem is based on the solutions from the subproblems. y = {85.215764226, 4.784235774}
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