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Simplifying 1950(x) = -15x2 + 600x + -1800 Reorder the terms: 1950x = -1800 + 600x + -15x2 Solving 1950x = -1800 + 600x + -15x2 Solving for variable 'x'. Reorder the terms: 1800 + 1950x + -600x + 15x2 = -1800 + 600x + -15x2 + 1800 + -600x + 15x2 Combine like terms: 1950x + -600x = 1350x 1800 + 1350x + 15x2 = -1800 + 600x + -15x2 + 1800 + -600x + 15x2 Reorder the terms: 1800 + 1350x + 15x2 = -1800 + 1800 + 600x + -600x + -15x2 + 15x2 Combine like terms: -1800 + 1800 = 0 1800 + 1350x + 15x2 = 0 + 600x + -600x + -15x2 + 15x2 1800 + 1350x + 15x2 = 600x + -600x + -15x2 + 15x2 Combine like terms: 600x + -600x = 0 1800 + 1350x + 15x2 = 0 + -15x2 + 15x2 1800 + 1350x + 15x2 = -15x2 + 15x2 Combine like terms: -15x2 + 15x2 = 0 1800 + 1350x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(120 + 90x + x2) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(120 + 90x + x2)' equal to zero and attempt to solve: Simplifying 120 + 90x + x2 = 0 Solving 120 + 90x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-120' to each side of the equation. 120 + 90x + -120 + x2 = 0 + -120 Reorder the terms: 120 + -120 + 90x + x2 = 0 + -120 Combine like terms: 120 + -120 = 0 0 + 90x + x2 = 0 + -120 90x + x2 = 0 + -120 Combine like terms: 0 + -120 = -120 90x + x2 = -120 The x term is 90x. Take half its coefficient (45). Square it (2025) and add it to both sides. Add '2025' to each side of the equation. 90x + 2025 + x2 = -120 + 2025 Reorder the terms: 2025 + 90x + x2 = -120 + 2025 Combine like terms: -120 + 2025 = 1905 2025 + 90x + x2 = 1905 Factor a perfect square on the left side: (x + 45)(x + 45) = 1905 Calculate the square root of the right side: 43.646305686 Break this problem into two subproblems by setting (x + 45) equal to 43.646305686 and -43.646305686.Subproblem 1
x + 45 = 43.646305686 Simplifying x + 45 = 43.646305686 Reorder the terms: 45 + x = 43.646305686 Solving 45 + x = 43.646305686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + x = 43.646305686 + -45 Combine like terms: 45 + -45 = 0 0 + x = 43.646305686 + -45 x = 43.646305686 + -45 Combine like terms: 43.646305686 + -45 = -1.353694314 x = -1.353694314 Simplifying x = -1.353694314Subproblem 2
x + 45 = -43.646305686 Simplifying x + 45 = -43.646305686 Reorder the terms: 45 + x = -43.646305686 Solving 45 + x = -43.646305686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + x = -43.646305686 + -45 Combine like terms: 45 + -45 = 0 0 + x = -43.646305686 + -45 x = -43.646305686 + -45 Combine like terms: -43.646305686 + -45 = -88.646305686 x = -88.646305686 Simplifying x = -88.646305686Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.353694314, -88.646305686}Solution
x = {-1.353694314, -88.646305686}
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