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Simplifying x3 + 3x2 + -105x = 0 Reorder the terms: -105x + 3x2 + x3 = 0 Solving -105x + 3x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-105 + 3x + 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 '(-105 + 3x + x2)' equal to zero and attempt to solve: Simplifying -105 + 3x + x2 = 0 Solving -105 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '105' to each side of the equation. -105 + 3x + 105 + x2 = 0 + 105 Reorder the terms: -105 + 105 + 3x + x2 = 0 + 105 Combine like terms: -105 + 105 = 0 0 + 3x + x2 = 0 + 105 3x + x2 = 0 + 105 Combine like terms: 0 + 105 = 105 3x + x2 = 105 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 105 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 105 + 2.25 Combine like terms: 105 + 2.25 = 107.25 2.25 + 3x + x2 = 107.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 107.25 Calculate the square root of the right side: 10.356157589 Break this problem into two subproblems by setting (x + 1.5) equal to 10.356157589 and -10.356157589.Subproblem 1
x + 1.5 = 10.356157589 Simplifying x + 1.5 = 10.356157589 Reorder the terms: 1.5 + x = 10.356157589 Solving 1.5 + x = 10.356157589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 10.356157589 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 10.356157589 + -1.5 x = 10.356157589 + -1.5 Combine like terms: 10.356157589 + -1.5 = 8.856157589 x = 8.856157589 Simplifying x = 8.856157589Subproblem 2
x + 1.5 = -10.356157589 Simplifying x + 1.5 = -10.356157589 Reorder the terms: 1.5 + x = -10.356157589 Solving 1.5 + x = -10.356157589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -10.356157589 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -10.356157589 + -1.5 x = -10.356157589 + -1.5 Combine like terms: -10.356157589 + -1.5 = -11.856157589 x = -11.856157589 Simplifying x = -11.856157589Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.856157589, -11.856157589}Solution
x = {0, 8.856157589, -11.856157589}
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