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Simplifying x3 + 4x2 + x = 0 Reorder the terms: x + 4x2 + x3 = 0 Solving x + 4x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(1 + 4x + 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 '(1 + 4x + x2)' equal to zero and attempt to solve: Simplifying 1 + 4x + x2 = 0 Solving 1 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 4x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 4x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x + x2 = 0 + -1 4x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 4x + x2 = -1 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -1 + 4 Reorder the terms: 4 + 4x + x2 = -1 + 4 Combine like terms: -1 + 4 = 3 4 + 4x + x2 = 3 Factor a perfect square on the left side: (x + 2)(x + 2) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + 2) equal to 1.732050808 and -1.732050808.Subproblem 1
x + 2 = 1.732050808 Simplifying x + 2 = 1.732050808 Reorder the terms: 2 + x = 1.732050808 Solving 2 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.732050808 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.732050808 + -2 x = 1.732050808 + -2 Combine like terms: 1.732050808 + -2 = -0.267949192 x = -0.267949192 Simplifying x = -0.267949192Subproblem 2
x + 2 = -1.732050808 Simplifying x + 2 = -1.732050808 Reorder the terms: 2 + x = -1.732050808 Solving 2 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.732050808 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.732050808 + -2 x = -1.732050808 + -2 Combine like terms: -1.732050808 + -2 = -3.732050808 x = -3.732050808 Simplifying x = -3.732050808Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.267949192, -3.732050808}Solution
x = {0, -0.267949192, -3.732050808}
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