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Simplifying x3 + 40x2 + 100x = 0 Reorder the terms: 100x + 40x2 + x3 = 0 Solving 100x + 40x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(100 + 40x + 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 '(100 + 40x + x2)' equal to zero and attempt to solve: Simplifying 100 + 40x + x2 = 0 Solving 100 + 40x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + 40x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + 40x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + 40x + x2 = 0 + -100 40x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 40x + x2 = -100 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = -100 + 400 Reorder the terms: 400 + 40x + x2 = -100 + 400 Combine like terms: -100 + 400 = 300 400 + 40x + x2 = 300 Factor a perfect square on the left side: (x + 20)(x + 20) = 300 Calculate the square root of the right side: 17.320508076 Break this problem into two subproblems by setting (x + 20) equal to 17.320508076 and -17.320508076.Subproblem 1
x + 20 = 17.320508076 Simplifying x + 20 = 17.320508076 Reorder the terms: 20 + x = 17.320508076 Solving 20 + x = 17.320508076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 17.320508076 + -20 Combine like terms: 20 + -20 = 0 0 + x = 17.320508076 + -20 x = 17.320508076 + -20 Combine like terms: 17.320508076 + -20 = -2.679491924 x = -2.679491924 Simplifying x = -2.679491924Subproblem 2
x + 20 = -17.320508076 Simplifying x + 20 = -17.320508076 Reorder the terms: 20 + x = -17.320508076 Solving 20 + x = -17.320508076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -17.320508076 + -20 Combine like terms: 20 + -20 = 0 0 + x = -17.320508076 + -20 x = -17.320508076 + -20 Combine like terms: -17.320508076 + -20 = -37.320508076 x = -37.320508076 Simplifying x = -37.320508076Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.679491924, -37.320508076}Solution
x = {0, -2.679491924, -37.320508076}
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