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Simplifying x4 + -2x3 + -36x2 = 0 Reorder the terms: -36x2 + -2x3 + x4 = 0 Solving -36x2 + -2x3 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-36 + -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 '(-36 + -2x + x2)' equal to zero and attempt to solve: Simplifying -36 + -2x + x2 = 0 Solving -36 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -2x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -2x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -2x + x2 = 0 + 36 -2x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -2x + x2 = 36 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 = 36 + 1 Reorder the terms: 1 + -2x + x2 = 36 + 1 Combine like terms: 36 + 1 = 37 1 + -2x + x2 = 37 Factor a perfect square on the left side: (x + -1)(x + -1) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (x + -1) equal to 6.08276253 and -6.08276253.Subproblem 1
x + -1 = 6.08276253 Simplifying x + -1 = 6.08276253 Reorder the terms: -1 + x = 6.08276253 Solving -1 + x = 6.08276253 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 = 6.08276253 + 1 Combine like terms: -1 + 1 = 0 0 + x = 6.08276253 + 1 x = 6.08276253 + 1 Combine like terms: 6.08276253 + 1 = 7.08276253 x = 7.08276253 Simplifying x = 7.08276253Subproblem 2
x + -1 = -6.08276253 Simplifying x + -1 = -6.08276253 Reorder the terms: -1 + x = -6.08276253 Solving -1 + x = -6.08276253 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 = -6.08276253 + 1 Combine like terms: -1 + 1 = 0 0 + x = -6.08276253 + 1 x = -6.08276253 + 1 Combine like terms: -6.08276253 + 1 = -5.08276253 x = -5.08276253 Simplifying x = -5.08276253Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.08276253, -5.08276253}Solution
x = {0, 7.08276253, -5.08276253}
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