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Simplifying x3 + 13x2 + 25x = 0 Reorder the terms: 25x + 13x2 + x3 = 0 Solving 25x + 13x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(25 + 13x + 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 '(25 + 13x + x2)' equal to zero and attempt to solve: Simplifying 25 + 13x + x2 = 0 Solving 25 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + 13x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + 13x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 13x + x2 = 0 + -25 13x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 13x + x2 = -25 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = -25 + 42.25 Reorder the terms: 42.25 + 13x + x2 = -25 + 42.25 Combine like terms: -25 + 42.25 = 17.25 42.25 + 13x + x2 = 17.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (x + 6.5) equal to 4.153311931 and -4.153311931.Subproblem 1
x + 6.5 = 4.153311931 Simplifying x + 6.5 = 4.153311931 Reorder the terms: 6.5 + x = 4.153311931 Solving 6.5 + x = 4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 4.153311931 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 4.153311931 + -6.5 x = 4.153311931 + -6.5 Combine like terms: 4.153311931 + -6.5 = -2.346688069 x = -2.346688069 Simplifying x = -2.346688069Subproblem 2
x + 6.5 = -4.153311931 Simplifying x + 6.5 = -4.153311931 Reorder the terms: 6.5 + x = -4.153311931 Solving 6.5 + x = -4.153311931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -4.153311931 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -4.153311931 + -6.5 x = -4.153311931 + -6.5 Combine like terms: -4.153311931 + -6.5 = -10.653311931 x = -10.653311931 Simplifying x = -10.653311931Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.346688069, -10.653311931}Solution
x = {0, -2.346688069, -10.653311931}
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