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Simplifying 5y2 + -30000y + -600000 = 0 Reorder the terms: -600000 + -30000y + 5y2 = 0 Solving -600000 + -30000y + 5y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5'. 5(-120000 + -6000y + y2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-120000 + -6000y + y2)' equal to zero and attempt to solve: Simplifying -120000 + -6000y + y2 = 0 Solving -120000 + -6000y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '120000' to each side of the equation. -120000 + -6000y + 120000 + y2 = 0 + 120000 Reorder the terms: -120000 + 120000 + -6000y + y2 = 0 + 120000 Combine like terms: -120000 + 120000 = 0 0 + -6000y + y2 = 0 + 120000 -6000y + y2 = 0 + 120000 Combine like terms: 0 + 120000 = 120000 -6000y + y2 = 120000 The y term is -6000y. Take half its coefficient (-3000). Square it (9000000) and add it to both sides. Add '9000000' to each side of the equation. -6000y + 9000000 + y2 = 120000 + 9000000 Reorder the terms: 9000000 + -6000y + y2 = 120000 + 9000000 Combine like terms: 120000 + 9000000 = 9120000 9000000 + -6000y + y2 = 9120000 Factor a perfect square on the left side: (y + -3000)(y + -3000) = 9120000 Calculate the square root of the right side: 3019.933774108 Break this problem into two subproblems by setting (y + -3000) equal to 3019.933774108 and -3019.933774108.Subproblem 1
y + -3000 = 3019.933774108 Simplifying y + -3000 = 3019.933774108 Reorder the terms: -3000 + y = 3019.933774108 Solving -3000 + y = 3019.933774108 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3000' to each side of the equation. -3000 + 3000 + y = 3019.933774108 + 3000 Combine like terms: -3000 + 3000 = 0 0 + y = 3019.933774108 + 3000 y = 3019.933774108 + 3000 Combine like terms: 3019.933774108 + 3000 = 6019.933774108 y = 6019.933774108 Simplifying y = 6019.933774108Subproblem 2
y + -3000 = -3019.933774108 Simplifying y + -3000 = -3019.933774108 Reorder the terms: -3000 + y = -3019.933774108 Solving -3000 + y = -3019.933774108 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3000' to each side of the equation. -3000 + 3000 + y = -3019.933774108 + 3000 Combine like terms: -3000 + 3000 = 0 0 + y = -3019.933774108 + 3000 y = -3019.933774108 + 3000 Combine like terms: -3019.933774108 + 3000 = -19.933774108 y = -19.933774108 Simplifying y = -19.933774108Solution
The solution to the problem is based on the solutions from the subproblems. y = {6019.933774108, -19.933774108}Solution
y = {6019.933774108, -19.933774108}
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