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Simplifying x3 + -3x2 + -24x + -17x = 0 Reorder the terms: -24x + -17x + -3x2 + x3 = 0 Combine like terms: -24x + -17x = -41x -41x + -3x2 + x3 = 0 Solving -41x + -3x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-41 + -3x + 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 '(-41 + -3x + x2)' equal to zero and attempt to solve: Simplifying -41 + -3x + x2 = 0 Solving -41 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + -3x + 41 + x2 = 0 + 41 Reorder the terms: -41 + 41 + -3x + x2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + -3x + x2 = 0 + 41 -3x + x2 = 0 + 41 Combine like terms: 0 + 41 = 41 -3x + x2 = 41 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 41 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 41 + 2.25 Combine like terms: 41 + 2.25 = 43.25 2.25 + -3x + x2 = 43.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 43.25 Calculate the square root of the right side: 6.576473219 Break this problem into two subproblems by setting (x + -1.5) equal to 6.576473219 and -6.576473219.Subproblem 1
x + -1.5 = 6.576473219 Simplifying x + -1.5 = 6.576473219 Reorder the terms: -1.5 + x = 6.576473219 Solving -1.5 + x = 6.576473219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 6.576473219 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 6.576473219 + 1.5 x = 6.576473219 + 1.5 Combine like terms: 6.576473219 + 1.5 = 8.076473219 x = 8.076473219 Simplifying x = 8.076473219Subproblem 2
x + -1.5 = -6.576473219 Simplifying x + -1.5 = -6.576473219 Reorder the terms: -1.5 + x = -6.576473219 Solving -1.5 + x = -6.576473219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -6.576473219 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -6.576473219 + 1.5 x = -6.576473219 + 1.5 Combine like terms: -6.576473219 + 1.5 = -5.076473219 x = -5.076473219 Simplifying x = -5.076473219Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.076473219, -5.076473219}Solution
x = {0, 8.076473219, -5.076473219}
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