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Simplifying x3 + 8x2 + 2x = 0 Reorder the terms: 2x + 8x2 + x3 = 0 Solving 2x + 8x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(2 + 8x + x2) = 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 '(2 + 8x + x2)' equal to zero and attempt to solve: Simplifying 2 + 8x + x2 = 0 Solving 2 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 8x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 8x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 8x + x2 = 0 + -2 8x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 8x + x2 = -2 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -2 + 16 Reorder the terms: 16 + 8x + x2 = -2 + 16 Combine like terms: -2 + 16 = 14 16 + 8x + x2 = 14 Factor a perfect square on the left side: (x + 4)(x + 4) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + 4) equal to 3.741657387 and -3.741657387.Subproblem 1
x + 4 = 3.741657387 Simplifying x + 4 = 3.741657387 Reorder the terms: 4 + x = 3.741657387 Solving 4 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 3.741657387 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.741657387 + -4 x = 3.741657387 + -4 Combine like terms: 3.741657387 + -4 = -0.258342613 x = -0.258342613 Simplifying x = -0.258342613Subproblem 2
x + 4 = -3.741657387 Simplifying x + 4 = -3.741657387 Reorder the terms: 4 + x = -3.741657387 Solving 4 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -3.741657387 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.741657387 + -4 x = -3.741657387 + -4 Combine like terms: -3.741657387 + -4 = -7.741657387 x = -7.741657387 Simplifying x = -7.741657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.258342613, -7.741657387}Solution
x = {0, -0.258342613, -7.741657387}
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