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Simplifying 8x3 + 16x2 + 3x = 0 Reorder the terms: 3x + 16x2 + 8x3 = 0 Solving 3x + 16x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(3 + 16x + 8x2) = 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 '(3 + 16x + 8x2)' equal to zero and attempt to solve: Simplifying 3 + 16x + 8x2 = 0 Solving 3 + 16x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + 2x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 2x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 2x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 2x + x2 = 0 + -0.375 2x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 2x + x2 = -0.375 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.375 + 1 Reorder the terms: 1 + 2x + x2 = -0.375 + 1 Combine like terms: -0.375 + 1 = 0.625 1 + 2x + x2 = 0.625 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.625 Calculate the square root of the right side: 0.790569415 Break this problem into two subproblems by setting (x + 1) equal to 0.790569415 and -0.790569415.Subproblem 1
x + 1 = 0.790569415 Simplifying x + 1 = 0.790569415 Reorder the terms: 1 + x = 0.790569415 Solving 1 + x = 0.790569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.790569415 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.790569415 + -1 x = 0.790569415 + -1 Combine like terms: 0.790569415 + -1 = -0.209430585 x = -0.209430585 Simplifying x = -0.209430585Subproblem 2
x + 1 = -0.790569415 Simplifying x + 1 = -0.790569415 Reorder the terms: 1 + x = -0.790569415 Solving 1 + x = -0.790569415 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.790569415 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.790569415 + -1 x = -0.790569415 + -1 Combine like terms: -0.790569415 + -1 = -1.790569415 x = -1.790569415 Simplifying x = -1.790569415Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.209430585, -1.790569415}Solution
x = {0, -0.209430585, -1.790569415}
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