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Simplifying x3 + 2x2 + -19x = 0 Reorder the terms: -19x + 2x2 + x3 = 0 Solving -19x + 2x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-19 + 2x + 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 '(-19 + 2x + x2)' equal to zero and attempt to solve: Simplifying -19 + 2x + x2 = 0 Solving -19 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + 2x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + 2x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + 2x + x2 = 0 + 19 2x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 2x + x2 = 19 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 19 + 1 Reorder the terms: 1 + 2x + x2 = 19 + 1 Combine like terms: 19 + 1 = 20 1 + 2x + x2 = 20 Factor a perfect square on the left side: (x + 1)(x + 1) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + 1) equal to 4.472135955 and -4.472135955.Subproblem 1
x + 1 = 4.472135955 Simplifying x + 1 = 4.472135955 Reorder the terms: 1 + x = 4.472135955 Solving 1 + x = 4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.472135955 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.472135955 + -1 x = 4.472135955 + -1 Combine like terms: 4.472135955 + -1 = 3.472135955 x = 3.472135955 Simplifying x = 3.472135955Subproblem 2
x + 1 = -4.472135955 Simplifying x + 1 = -4.472135955 Reorder the terms: 1 + x = -4.472135955 Solving 1 + x = -4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.472135955 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.472135955 + -1 x = -4.472135955 + -1 Combine like terms: -4.472135955 + -1 = -5.472135955 x = -5.472135955 Simplifying x = -5.472135955Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.472135955, -5.472135955}Solution
x = {0, 3.472135955, -5.472135955}
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