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Simplifying 0 = 900x + -60x2 + -1x3 Solving 0 = 900x + -60x2 + -1x3 Solving for variable 'x'. Remove the zero: -900x + 60x2 + x3 = 900x + -60x2 + -1x3 + -900x + 60x2 + x3 Reorder the terms: -900x + 60x2 + x3 = 900x + -900x + -60x2 + 60x2 + -1x3 + x3 Combine like terms: 900x + -900x = 0 -900x + 60x2 + x3 = 0 + -60x2 + 60x2 + -1x3 + x3 -900x + 60x2 + x3 = -60x2 + 60x2 + -1x3 + x3 Combine like terms: -60x2 + 60x2 = 0 -900x + 60x2 + x3 = 0 + -1x3 + x3 -900x + 60x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 -900x + 60x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-900 + 60x + x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-900 + 60x + x2)' equal to zero and attempt to solve: Simplifying -900 + 60x + x2 = 0 Solving -900 + 60x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '900' to each side of the equation. -900 + 60x + 900 + x2 = 0 + 900 Reorder the terms: -900 + 900 + 60x + x2 = 0 + 900 Combine like terms: -900 + 900 = 0 0 + 60x + x2 = 0 + 900 60x + x2 = 0 + 900 Combine like terms: 0 + 900 = 900 60x + x2 = 900 The x term is 60x. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60x + 900 + x2 = 900 + 900 Reorder the terms: 900 + 60x + x2 = 900 + 900 Combine like terms: 900 + 900 = 1800 900 + 60x + x2 = 1800 Factor a perfect square on the left side: (x + 30)(x + 30) = 1800 Calculate the square root of the right side: 42.426406871 Break this problem into two subproblems by setting (x + 30) equal to 42.426406871 and -42.426406871.Subproblem 1
x + 30 = 42.426406871 Simplifying x + 30 = 42.426406871 Reorder the terms: 30 + x = 42.426406871 Solving 30 + x = 42.426406871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 42.426406871 + -30 Combine like terms: 30 + -30 = 0 0 + x = 42.426406871 + -30 x = 42.426406871 + -30 Combine like terms: 42.426406871 + -30 = 12.426406871 x = 12.426406871 Simplifying x = 12.426406871Subproblem 2
x + 30 = -42.426406871 Simplifying x + 30 = -42.426406871 Reorder the terms: 30 + x = -42.426406871 Solving 30 + x = -42.426406871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = -42.426406871 + -30 Combine like terms: 30 + -30 = 0 0 + x = -42.426406871 + -30 x = -42.426406871 + -30 Combine like terms: -42.426406871 + -30 = -72.426406871 x = -72.426406871 Simplifying x = -72.426406871Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.426406871, -72.426406871}Solution
x = {0, 12.426406871, -72.426406871}
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