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Simplifying x3 + 19x2 + -5x = 0 Reorder the terms: -5x + 19x2 + x3 = 0 Solving -5x + 19x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-5 + 19x + 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 '(-5 + 19x + x2)' equal to zero and attempt to solve: Simplifying -5 + 19x + x2 = 0 Solving -5 + 19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 19x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 19x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 19x + x2 = 0 + 5 19x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 19x + x2 = 5 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = 5 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 5 + 90.25 Combine like terms: 5 + 90.25 = 95.25 90.25 + 19x + x2 = 95.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 95.25 Calculate the square root of the right side: 9.759610648 Break this problem into two subproblems by setting (x + 9.5) equal to 9.759610648 and -9.759610648.Subproblem 1
x + 9.5 = 9.759610648 Simplifying x + 9.5 = 9.759610648 Reorder the terms: 9.5 + x = 9.759610648 Solving 9.5 + x = 9.759610648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 9.759610648 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 9.759610648 + -9.5 x = 9.759610648 + -9.5 Combine like terms: 9.759610648 + -9.5 = 0.259610648 x = 0.259610648 Simplifying x = 0.259610648Subproblem 2
x + 9.5 = -9.759610648 Simplifying x + 9.5 = -9.759610648 Reorder the terms: 9.5 + x = -9.759610648 Solving 9.5 + x = -9.759610648 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -9.759610648 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -9.759610648 + -9.5 x = -9.759610648 + -9.5 Combine like terms: -9.759610648 + -9.5 = -19.259610648 x = -19.259610648 Simplifying x = -19.259610648Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.259610648, -19.259610648}Solution
x = {0, 0.259610648, -19.259610648}
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