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Simplifying x4 + -4x3 + -3x2 = 0 Reorder the terms: -3x2 + -4x3 + x4 = 0 Solving -3x2 + -4x3 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-3 + -4x + x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-3 + -4x + x2)' equal to zero and attempt to solve: Simplifying -3 + -4x + x2 = 0 Solving -3 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -4x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -4x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4x + x2 = 0 + 3 -4x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -4x + x2 = 3 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 = 3 + 4 Reorder the terms: 4 + -4x + x2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + -4x + x2 = 7 Factor a perfect square on the left side: (x + -2)(x + -2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + -2) equal to 2.645751311 and -2.645751311.Subproblem 1
x + -2 = 2.645751311 Simplifying x + -2 = 2.645751311 Reorder the terms: -2 + x = 2.645751311 Solving -2 + x = 2.645751311 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 = 2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.645751311 + 2 x = 2.645751311 + 2 Combine like terms: 2.645751311 + 2 = 4.645751311 x = 4.645751311 Simplifying x = 4.645751311Subproblem 2
x + -2 = -2.645751311 Simplifying x + -2 = -2.645751311 Reorder the terms: -2 + x = -2.645751311 Solving -2 + x = -2.645751311 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 = -2.645751311 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.645751311 + 2 x = -2.645751311 + 2 Combine like terms: -2.645751311 + 2 = -0.645751311 x = -0.645751311 Simplifying x = -0.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.645751311, -0.645751311}Solution
x = {0, 4.645751311, -0.645751311}
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