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Simplifying 46x3 + 43x2 + 5x = 0 Reorder the terms: 5x + 43x2 + 46x3 = 0 Solving 5x + 43x2 + 46x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(5 + 43x + 46x2) = 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 '(5 + 43x + 46x2)' equal to zero and attempt to solve: Simplifying 5 + 43x + 46x2 = 0 Solving 5 + 43x + 46x2 = 0 Begin completing the square. Divide all terms by 46 the coefficient of the squared term: Divide each side by '46'. 0.1086956522 + 0.9347826087x + x2 = 0 Move the constant term to the right: Add '-0.1086956522' to each side of the equation. 0.1086956522 + 0.9347826087x + -0.1086956522 + x2 = 0 + -0.1086956522 Reorder the terms: 0.1086956522 + -0.1086956522 + 0.9347826087x + x2 = 0 + -0.1086956522 Combine like terms: 0.1086956522 + -0.1086956522 = 0.0000000000 0.0000000000 + 0.9347826087x + x2 = 0 + -0.1086956522 0.9347826087x + x2 = 0 + -0.1086956522 Combine like terms: 0 + -0.1086956522 = -0.1086956522 0.9347826087x + x2 = -0.1086956522 The x term is 0.9347826087x. Take half its coefficient (0.4673913044). Square it (0.2184546314) and add it to both sides. Add '0.2184546314' to each side of the equation. 0.9347826087x + 0.2184546314 + x2 = -0.1086956522 + 0.2184546314 Reorder the terms: 0.2184546314 + 0.9347826087x + x2 = -0.1086956522 + 0.2184546314 Combine like terms: -0.1086956522 + 0.2184546314 = 0.1097589792 0.2184546314 + 0.9347826087x + x2 = 0.1097589792 Factor a perfect square on the left side: (x + 0.4673913044)(x + 0.4673913044) = 0.1097589792 Calculate the square root of the right side: 0.331298927 Break this problem into two subproblems by setting (x + 0.4673913044) equal to 0.331298927 and -0.331298927.Subproblem 1
x + 0.4673913044 = 0.331298927 Simplifying x + 0.4673913044 = 0.331298927 Reorder the terms: 0.4673913044 + x = 0.331298927 Solving 0.4673913044 + x = 0.331298927 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4673913044' to each side of the equation. 0.4673913044 + -0.4673913044 + x = 0.331298927 + -0.4673913044 Combine like terms: 0.4673913044 + -0.4673913044 = 0.0000000000 0.0000000000 + x = 0.331298927 + -0.4673913044 x = 0.331298927 + -0.4673913044 Combine like terms: 0.331298927 + -0.4673913044 = -0.1360923774 x = -0.1360923774 Simplifying x = -0.1360923774Subproblem 2
x + 0.4673913044 = -0.331298927 Simplifying x + 0.4673913044 = -0.331298927 Reorder the terms: 0.4673913044 + x = -0.331298927 Solving 0.4673913044 + x = -0.331298927 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4673913044' to each side of the equation. 0.4673913044 + -0.4673913044 + x = -0.331298927 + -0.4673913044 Combine like terms: 0.4673913044 + -0.4673913044 = 0.0000000000 0.0000000000 + x = -0.331298927 + -0.4673913044 x = -0.331298927 + -0.4673913044 Combine like terms: -0.331298927 + -0.4673913044 = -0.7986902314 x = -0.7986902314 Simplifying x = -0.7986902314Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1360923774, -0.7986902314}Solution
x = {0, -0.1360923774, -0.7986902314}
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