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Simplifying 40x3 + 15x2 + -4x = 0 Reorder the terms: -4x + 15x2 + 40x3 = 0 Solving -4x + 15x2 + 40x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + 15x + 40x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-4 + 15x + 40x2)' equal to zero and attempt to solve: Simplifying -4 + 15x + 40x2 = 0 Solving -4 + 15x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -0.1 + 0.375x + x2 = 0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 0.375x + 0.1 + x2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + 0.375x + x2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 0.375x + x2 = 0 + 0.1 0.375x + x2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 0.375x + x2 = 0.1 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = 0.1 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 0.1 + 0.03515625 Combine like terms: 0.1 + 0.03515625 = 0.13515625 0.03515625 + 0.375x + x2 = 0.13515625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 0.13515625 Calculate the square root of the right side: 0.367636029 Break this problem into two subproblems by setting (x + 0.1875) equal to 0.367636029 and -0.367636029.Subproblem 1
x + 0.1875 = 0.367636029 Simplifying x + 0.1875 = 0.367636029 Reorder the terms: 0.1875 + x = 0.367636029 Solving 0.1875 + x = 0.367636029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 0.367636029 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 0.367636029 + -0.1875 x = 0.367636029 + -0.1875 Combine like terms: 0.367636029 + -0.1875 = 0.180136029 x = 0.180136029 Simplifying x = 0.180136029Subproblem 2
x + 0.1875 = -0.367636029 Simplifying x + 0.1875 = -0.367636029 Reorder the terms: 0.1875 + x = -0.367636029 Solving 0.1875 + x = -0.367636029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -0.367636029 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -0.367636029 + -0.1875 x = -0.367636029 + -0.1875 Combine like terms: -0.367636029 + -0.1875 = -0.555136029 x = -0.555136029 Simplifying x = -0.555136029Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.180136029, -0.555136029}Solution
x = {0, 0.180136029, -0.555136029}
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