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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 = 2432.6923077 2025 + -90y + y2 = 2432.6923077 Factor a perfect square on the left side: (y + -45)(y + -45) = 2432.6923077 Calculate the square root of the right side: 49.32233072 Break this problem into two subproblems by setting (y + -45) equal to 49.32233072 and -49.32233072.Subproblem 1
y + -45 = 49.32233072 Simplifying y + -45 = 49.32233072 Reorder the terms: -45 + y = 49.32233072 Solving -45 + y = 49.32233072 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 = 49.32233072 + 45 Combine like terms: -45 + 45 = 0 0 + y = 49.32233072 + 45 y = 49.32233072 + 45 Combine like terms: 49.32233072 + 45 = 94.32233072 y = 94.32233072 Simplifying y = 94.32233072Subproblem 2
y + -45 = -49.32233072 Simplifying y + -45 = -49.32233072 Reorder the terms: -45 + y = -49.32233072 Solving -45 + y = -49.32233072 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 = -49.32233072 + 45 Combine like terms: -45 + 45 = 0 0 + y = -49.32233072 + 45 y = -49.32233072 + 45 Combine like terms: -49.32233072 + 45 = -4.32233072 y = -4.32233072 Simplifying y = -4.32233072Solution
The solution to the problem is based on the solutions from the subproblems. y = {94.32233072, -4.32233072}
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