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Simplifying 2x4 + -10x3 + -1x2 = 0 Reorder the terms: -1x2 + -10x3 + 2x4 = 0 Solving -1x2 + -10x3 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-1 + -10x + 2x2) = 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 '(-1 + -10x + 2x2)' equal to zero and attempt to solve: Simplifying -1 + -10x + 2x2 = 0 Solving -1 + -10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -5x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -5x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -5x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -5x + x2 = 0 + 0.5 -5x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -5x + x2 = 0.5 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 0.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 0.5 + 6.25 Combine like terms: 0.5 + 6.25 = 6.75 6.25 + -5x + x2 = 6.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (x + -2.5) equal to 2.598076211 and -2.598076211.Subproblem 1
x + -2.5 = 2.598076211 Simplifying x + -2.5 = 2.598076211 Reorder the terms: -2.5 + x = 2.598076211 Solving -2.5 + x = 2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 2.598076211 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.598076211 + 2.5 x = 2.598076211 + 2.5 Combine like terms: 2.598076211 + 2.5 = 5.098076211 x = 5.098076211 Simplifying x = 5.098076211Subproblem 2
x + -2.5 = -2.598076211 Simplifying x + -2.5 = -2.598076211 Reorder the terms: -2.5 + x = -2.598076211 Solving -2.5 + x = -2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -2.598076211 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.598076211 + 2.5 x = -2.598076211 + 2.5 Combine like terms: -2.598076211 + 2.5 = -0.098076211 x = -0.098076211 Simplifying x = -0.098076211Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.098076211, -0.098076211}Solution
x = {0, 5.098076211, -0.098076211}
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