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Simplifying 4x4 + -52x3 + 4x2 = 0 Reorder the terms: 4x2 + -52x3 + 4x4 = 0 Solving 4x2 + -52x3 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x2'. 4x2(1 + -13x + x2) = 0 Ignore the factor 4.Subproblem 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 '(1 + -13x + x2)' equal to zero and attempt to solve: Simplifying 1 + -13x + x2 = 0 Solving 1 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -13x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -13x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -13x + x2 = 0 + -1 -13x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -13x + x2 = -1 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -1 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -1 + 42.25 Combine like terms: -1 + 42.25 = 41.25 42.25 + -13x + x2 = 41.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (x + -6.5) equal to 6.422616289 and -6.422616289.Subproblem 1
x + -6.5 = 6.422616289 Simplifying x + -6.5 = 6.422616289 Reorder the terms: -6.5 + x = 6.422616289 Solving -6.5 + x = 6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 6.422616289 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 6.422616289 + 6.5 x = 6.422616289 + 6.5 Combine like terms: 6.422616289 + 6.5 = 12.922616289 x = 12.922616289 Simplifying x = 12.922616289Subproblem 2
x + -6.5 = -6.422616289 Simplifying x + -6.5 = -6.422616289 Reorder the terms: -6.5 + x = -6.422616289 Solving -6.5 + x = -6.422616289 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -6.422616289 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -6.422616289 + 6.5 x = -6.422616289 + 6.5 Combine like terms: -6.422616289 + 6.5 = 0.077383711 x = 0.077383711 Simplifying x = 0.077383711Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.922616289, 0.077383711}Solution
x = {0, 12.922616289, 0.077383711}
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