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Simplifying x4 + -10x3 + 3x2 = 0 Reorder the terms: 3x2 + -10x3 + x4 = 0 Solving 3x2 + -10x3 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(3 + -10x + 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 '(3 + -10x + x2)' equal to zero and attempt to solve: Simplifying 3 + -10x + x2 = 0 Solving 3 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -10x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -10x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -10x + x2 = 0 + -3 -10x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -10x + x2 = -3 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -3 + 25 Reorder the terms: 25 + -10x + x2 = -3 + 25 Combine like terms: -3 + 25 = 22 25 + -10x + x2 = 22 Factor a perfect square on the left side: (x + -5)(x + -5) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (x + -5) equal to 4.69041576 and -4.69041576.Subproblem 1
x + -5 = 4.69041576 Simplifying x + -5 = 4.69041576 Reorder the terms: -5 + x = 4.69041576 Solving -5 + x = 4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.69041576 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.69041576 + 5 x = 4.69041576 + 5 Combine like terms: 4.69041576 + 5 = 9.69041576 x = 9.69041576 Simplifying x = 9.69041576Subproblem 2
x + -5 = -4.69041576 Simplifying x + -5 = -4.69041576 Reorder the terms: -5 + x = -4.69041576 Solving -5 + x = -4.69041576 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.69041576 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.69041576 + 5 x = -4.69041576 + 5 Combine like terms: -4.69041576 + 5 = 0.30958424 x = 0.30958424 Simplifying x = 0.30958424Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.69041576, 0.30958424}Solution
x = {0, 9.69041576, 0.30958424}
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