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Simplifying x4 + -2x3 + -5x2 = 0 Reorder the terms: -5x2 + -2x3 + x4 = 0 Solving -5x2 + -2x3 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-5 + -2x + 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 '(-5 + -2x + x2)' equal to zero and attempt to solve: Simplifying -5 + -2x + x2 = 0 Solving -5 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -2x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -2x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x + x2 = 0 + 5 -2x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2x + x2 = 5 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 = 5 + 1 Reorder the terms: 1 + -2x + x2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + -2x + x2 = 6 Factor a perfect square on the left side: (x + -1)(x + -1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -1) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -1 = 2.449489743 Simplifying x + -1 = 2.449489743 Reorder the terms: -1 + x = 2.449489743 Solving -1 + x = 2.449489743 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 = 2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.449489743 + 1 x = 2.449489743 + 1 Combine like terms: 2.449489743 + 1 = 3.449489743 x = 3.449489743 Simplifying x = 3.449489743Subproblem 2
x + -1 = -2.449489743 Simplifying x + -1 = -2.449489743 Reorder the terms: -1 + x = -2.449489743 Solving -1 + x = -2.449489743 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 = -2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.449489743 + 1 x = -2.449489743 + 1 Combine like terms: -2.449489743 + 1 = -1.449489743 x = -1.449489743 Simplifying x = -1.449489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.449489743, -1.449489743}Solution
x = {0, 3.449489743, -1.449489743}
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