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Simplifying 20x3 + -1x2 + -20x = 0 Reorder the terms: -20x + -1x2 + 20x3 = 0 Solving -20x + -1x2 + 20x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-20 + -1x + 20x2) = 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 '(-20 + -1x + 20x2)' equal to zero and attempt to solve: Simplifying -20 + -1x + 20x2 = 0 Solving -20 + -1x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -1 + -0.05x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.05x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.05x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.05x + x2 = 0 + 1 -0.05x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.05x + x2 = 1 The x term is -0.05x. Take half its coefficient (-0.025). Square it (0.000625) and add it to both sides. Add '0.000625' to each side of the equation. -0.05x + 0.000625 + x2 = 1 + 0.000625 Reorder the terms: 0.000625 + -0.05x + x2 = 1 + 0.000625 Combine like terms: 1 + 0.000625 = 1.000625 0.000625 + -0.05x + x2 = 1.000625 Factor a perfect square on the left side: (x + -0.025)(x + -0.025) = 1.000625 Calculate the square root of the right side: 1.000312451 Break this problem into two subproblems by setting (x + -0.025) equal to 1.000312451 and -1.000312451.Subproblem 1
x + -0.025 = 1.000312451 Simplifying x + -0.025 = 1.000312451 Reorder the terms: -0.025 + x = 1.000312451 Solving -0.025 + x = 1.000312451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.025' to each side of the equation. -0.025 + 0.025 + x = 1.000312451 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + x = 1.000312451 + 0.025 x = 1.000312451 + 0.025 Combine like terms: 1.000312451 + 0.025 = 1.025312451 x = 1.025312451 Simplifying x = 1.025312451Subproblem 2
x + -0.025 = -1.000312451 Simplifying x + -0.025 = -1.000312451 Reorder the terms: -0.025 + x = -1.000312451 Solving -0.025 + x = -1.000312451 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.025' to each side of the equation. -0.025 + 0.025 + x = -1.000312451 + 0.025 Combine like terms: -0.025 + 0.025 = 0.000 0.000 + x = -1.000312451 + 0.025 x = -1.000312451 + 0.025 Combine like terms: -1.000312451 + 0.025 = -0.975312451 x = -0.975312451 Simplifying x = -0.975312451Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.025312451, -0.975312451}Solution
x = {0, 1.025312451, -0.975312451}
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