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Simplifying 0 = 5x3 + -11x2 + 4x Reorder the terms: 0 = 4x + -11x2 + 5x3 Solving 0 = 4x + -11x2 + 5x3 Solving for variable 'x'. Remove the zero: -4x + 11x2 + -5x3 = 4x + -11x2 + 5x3 + -4x + 11x2 + -5x3 Reorder the terms: -4x + 11x2 + -5x3 = 4x + -4x + -11x2 + 11x2 + 5x3 + -5x3 Combine like terms: 4x + -4x = 0 -4x + 11x2 + -5x3 = 0 + -11x2 + 11x2 + 5x3 + -5x3 -4x + 11x2 + -5x3 = -11x2 + 11x2 + 5x3 + -5x3 Combine like terms: -11x2 + 11x2 = 0 -4x + 11x2 + -5x3 = 0 + 5x3 + -5x3 -4x + 11x2 + -5x3 = 5x3 + -5x3 Combine like terms: 5x3 + -5x3 = 0 -4x + 11x2 + -5x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + 11x + -5x2) = 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 '(-4 + 11x + -5x2)' equal to zero and attempt to solve: Simplifying -4 + 11x + -5x2 = 0 Solving -4 + 11x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 0.8 + -2.2x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -2.2x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -2.2x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -2.2x + x2 = 0 + -0.8 -2.2x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -2.2x + x2 = -0.8 The x term is -2.2x. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2x + 1.21 + x2 = -0.8 + 1.21 Reorder the terms: 1.21 + -2.2x + x2 = -0.8 + 1.21 Combine like terms: -0.8 + 1.21 = 0.41 1.21 + -2.2x + x2 = 0.41 Factor a perfect square on the left side: (x + -1.1)(x + -1.1) = 0.41 Calculate the square root of the right side: 0.640312424 Break this problem into two subproblems by setting (x + -1.1) equal to 0.640312424 and -0.640312424.Subproblem 1
x + -1.1 = 0.640312424 Simplifying x + -1.1 = 0.640312424 Reorder the terms: -1.1 + x = 0.640312424 Solving -1.1 + x = 0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = 0.640312424 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 0.640312424 + 1.1 x = 0.640312424 + 1.1 Combine like terms: 0.640312424 + 1.1 = 1.740312424 x = 1.740312424 Simplifying x = 1.740312424Subproblem 2
x + -1.1 = -0.640312424 Simplifying x + -1.1 = -0.640312424 Reorder the terms: -1.1 + x = -0.640312424 Solving -1.1 + x = -0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = -0.640312424 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -0.640312424 + 1.1 x = -0.640312424 + 1.1 Combine like terms: -0.640312424 + 1.1 = 0.459687576 x = 0.459687576 Simplifying x = 0.459687576Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.740312424, 0.459687576}Solution
x = {0, 1.740312424, 0.459687576}
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