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Simplifying 4x4 + -11x3 + -13x2 = 0 Reorder the terms: -13x2 + -11x3 + 4x4 = 0 Solving -13x2 + -11x3 + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-13 + -11x + 4x2) = 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 '(-13 + -11x + 4x2)' equal to zero and attempt to solve: Simplifying -13 + -11x + 4x2 = 0 Solving -13 + -11x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.25 + -2.75x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + -2.75x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + -2.75x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + -2.75x + x2 = 0 + 3.25 -2.75x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 -2.75x + x2 = 3.25 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = 3.25 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 3.25 + 1.890625 Combine like terms: 3.25 + 1.890625 = 5.140625 1.890625 + -2.75x + x2 = 5.140625 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 5.140625 Calculate the square root of the right side: 2.267294643 Break this problem into two subproblems by setting (x + -1.375) equal to 2.267294643 and -2.267294643.Subproblem 1
x + -1.375 = 2.267294643 Simplifying x + -1.375 = 2.267294643 Reorder the terms: -1.375 + x = 2.267294643 Solving -1.375 + x = 2.267294643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 2.267294643 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 2.267294643 + 1.375 x = 2.267294643 + 1.375 Combine like terms: 2.267294643 + 1.375 = 3.642294643 x = 3.642294643 Simplifying x = 3.642294643Subproblem 2
x + -1.375 = -2.267294643 Simplifying x + -1.375 = -2.267294643 Reorder the terms: -1.375 + x = -2.267294643 Solving -1.375 + x = -2.267294643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -2.267294643 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -2.267294643 + 1.375 x = -2.267294643 + 1.375 Combine like terms: -2.267294643 + 1.375 = -0.892294643 x = -0.892294643 Simplifying x = -0.892294643Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.642294643, -0.892294643}Solution
x = {0, 3.642294643, -0.892294643}
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