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Simplifying (-9 + 90y + -1) * y + 9y + -90 = 0 Reorder the terms: (-9 + -1 + 90y) * y + 9y + -90 = 0 Combine like terms: -9 + -1 = -10 (-10 + 90y) * y + 9y + -90 = 0 Reorder the terms for easier multiplication: y(-10 + 90y) + 9y + -90 = 0 (-10 * y + 90y * y) + 9y + -90 = 0 (-10y + 90y2) + 9y + -90 = 0 Reorder the terms: -90 + -10y + 9y + 90y2 = 0 Combine like terms: -10y + 9y = -1y -90 + -1y + 90y2 = 0 Solving -90 + -1y + 90y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 90 the coefficient of the squared term: Divide each side by '90'. -1 + -0.01111111111y + y2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.01111111111y + 1 + y2 = 0 + 1 Reorder the terms: -1 + 1 + -0.01111111111y + y2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.01111111111y + y2 = 0 + 1 -0.01111111111y + y2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.01111111111y + y2 = 1 The y term is -0.01111111111y. Take half its coefficient (-0.005555555555). Square it (0.00003086419752) and add it to both sides. Add '0.00003086419752' to each side of the equation. -0.01111111111y + 0.00003086419752 + y2 = 1 + 0.00003086419752 Reorder the terms: 0.00003086419752 + -0.01111111111y + y2 = 1 + 0.00003086419752 Combine like terms: 1 + 0.00003086419752 = 1.00003086419752 0.00003086419752 + -0.01111111111y + y2 = 1.00003086419752 Factor a perfect square on the left side: (y + -0.005555555555)(y + -0.005555555555) = 1.00003086419752 Calculate the square root of the right side: 1.000015432 Break this problem into two subproblems by setting (y + -0.005555555555) equal to 1.000015432 and -1.000015432.Subproblem 1
y + -0.005555555555 = 1.000015432 Simplifying y + -0.005555555555 = 1.000015432 Reorder the terms: -0.005555555555 + y = 1.000015432 Solving -0.005555555555 + y = 1.000015432 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.005555555555' to each side of the equation. -0.005555555555 + 0.005555555555 + y = 1.000015432 + 0.005555555555 Combine like terms: -0.005555555555 + 0.005555555555 = 0.000000000000 0.000000000000 + y = 1.000015432 + 0.005555555555 y = 1.000015432 + 0.005555555555 Combine like terms: 1.000015432 + 0.005555555555 = 1.005570987555 y = 1.005570987555 Simplifying y = 1.005570987555Subproblem 2
y + -0.005555555555 = -1.000015432 Simplifying y + -0.005555555555 = -1.000015432 Reorder the terms: -0.005555555555 + y = -1.000015432 Solving -0.005555555555 + y = -1.000015432 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.005555555555' to each side of the equation. -0.005555555555 + 0.005555555555 + y = -1.000015432 + 0.005555555555 Combine like terms: -0.005555555555 + 0.005555555555 = 0.000000000000 0.000000000000 + y = -1.000015432 + 0.005555555555 y = -1.000015432 + 0.005555555555 Combine like terms: -1.000015432 + 0.005555555555 = -0.994459876445 y = -0.994459876445 Simplifying y = -0.994459876445Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.005570987555, -0.994459876445}
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