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Simplifying 7.29y2 + -3028y + 100170 = 0 Reorder the terms: 100170 + -3028y + 7.29y2 = 0 Solving 100170 + -3028y + 7.29y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 7.29 the coefficient of the squared term: Divide each side by '7.29'. 13740.74074 + -415.3635117y + y2 = 0 Move the constant term to the right: Add '-13740.74074' to each side of the equation. 13740.74074 + -415.3635117y + -13740.74074 + y2 = 0 + -13740.74074 Reorder the terms: 13740.74074 + -13740.74074 + -415.3635117y + y2 = 0 + -13740.74074 Combine like terms: 13740.74074 + -13740.74074 = 0.00000 0.00000 + -415.3635117y + y2 = 0 + -13740.74074 -415.3635117y + y2 = 0 + -13740.74074 Combine like terms: 0 + -13740.74074 = -13740.74074 -415.3635117y + y2 = -13740.74074 The y term is -415.3635117y. Take half its coefficient (-207.6817559). Square it (43131.71173) and add it to both sides. Add '43131.71173' to each side of the equation. -415.3635117y + 43131.71173 + y2 = -13740.74074 + 43131.71173 Reorder the terms: 43131.71173 + -415.3635117y + y2 = -13740.74074 + 43131.71173 Combine like terms: -13740.74074 + 43131.71173 = 29390.97099 43131.71173 + -415.3635117y + y2 = 29390.97099 Factor a perfect square on the left side: (y + -207.6817559)(y + -207.6817559) = 29390.97099 Calculate the square root of the right side: 171.437950845 Break this problem into two subproblems by setting (y + -207.6817559) equal to 171.437950845 and -171.437950845.Subproblem 1
y + -207.6817559 = 171.437950845 Simplifying y + -207.6817559 = 171.437950845 Reorder the terms: -207.6817559 + y = 171.437950845 Solving -207.6817559 + y = 171.437950845 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '207.6817559' to each side of the equation. -207.6817559 + 207.6817559 + y = 171.437950845 + 207.6817559 Combine like terms: -207.6817559 + 207.6817559 = 0.0000000 0.0000000 + y = 171.437950845 + 207.6817559 y = 171.437950845 + 207.6817559 Combine like terms: 171.437950845 + 207.6817559 = 379.119706745 y = 379.119706745 Simplifying y = 379.119706745Subproblem 2
y + -207.6817559 = -171.437950845 Simplifying y + -207.6817559 = -171.437950845 Reorder the terms: -207.6817559 + y = -171.437950845 Solving -207.6817559 + y = -171.437950845 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '207.6817559' to each side of the equation. -207.6817559 + 207.6817559 + y = -171.437950845 + 207.6817559 Combine like terms: -207.6817559 + 207.6817559 = 0.0000000 0.0000000 + y = -171.437950845 + 207.6817559 y = -171.437950845 + 207.6817559 Combine like terms: -171.437950845 + 207.6817559 = 36.243805055 y = 36.243805055 Simplifying y = 36.243805055Solution
The solution to the problem is based on the solutions from the subproblems. y = {379.119706745, 36.243805055}
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