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Simplifying x3 + 19x2 + 12x = 0 Reorder the terms: 12x + 19x2 + x3 = 0 Solving 12x + 19x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(12 + 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 '(12 + 19x + x2)' equal to zero and attempt to solve: Simplifying 12 + 19x + x2 = 0 Solving 12 + 19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + 19x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + 19x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 19x + x2 = 0 + -12 19x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 19x + x2 = -12 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 = -12 + 90.25 Reorder the terms: 90.25 + 19x + x2 = -12 + 90.25 Combine like terms: -12 + 90.25 = 78.25 90.25 + 19x + x2 = 78.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (x + 9.5) equal to 8.845903006 and -8.845903006.Subproblem 1
x + 9.5 = 8.845903006 Simplifying x + 9.5 = 8.845903006 Reorder the terms: 9.5 + x = 8.845903006 Solving 9.5 + x = 8.845903006 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 = 8.845903006 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 8.845903006 + -9.5 x = 8.845903006 + -9.5 Combine like terms: 8.845903006 + -9.5 = -0.654096994 x = -0.654096994 Simplifying x = -0.654096994Subproblem 2
x + 9.5 = -8.845903006 Simplifying x + 9.5 = -8.845903006 Reorder the terms: 9.5 + x = -8.845903006 Solving 9.5 + x = -8.845903006 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 = -8.845903006 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -8.845903006 + -9.5 x = -8.845903006 + -9.5 Combine like terms: -8.845903006 + -9.5 = -18.345903006 x = -18.345903006 Simplifying x = -18.345903006Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.654096994, -18.345903006}Solution
x = {0, -0.654096994, -18.345903006}
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