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Simplifying x3 + -3x2 + -24x + 17x = 0 Reorder the terms: -24x + 17x + -3x2 + x3 = 0 Combine like terms: -24x + 17x = -7x -7x + -3x2 + x3 = 0 Solving -7x + -3x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-7 + -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 '(-7 + -3x + x2)' equal to zero and attempt to solve: Simplifying -7 + -3x + x2 = 0 Solving -7 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -3x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -3x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3x + x2 = 0 + 7 -3x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -3x + x2 = 7 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 = 7 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 7 + 2.25 Combine like terms: 7 + 2.25 = 9.25 2.25 + -3x + x2 = 9.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (x + -1.5) equal to 3.041381265 and -3.041381265.Subproblem 1
x + -1.5 = 3.041381265 Simplifying x + -1.5 = 3.041381265 Reorder the terms: -1.5 + x = 3.041381265 Solving -1.5 + x = 3.041381265 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 = 3.041381265 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.041381265 + 1.5 x = 3.041381265 + 1.5 Combine like terms: 3.041381265 + 1.5 = 4.541381265 x = 4.541381265 Simplifying x = 4.541381265Subproblem 2
x + -1.5 = -3.041381265 Simplifying x + -1.5 = -3.041381265 Reorder the terms: -1.5 + x = -3.041381265 Solving -1.5 + x = -3.041381265 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 = -3.041381265 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.041381265 + 1.5 x = -3.041381265 + 1.5 Combine like terms: -3.041381265 + 1.5 = -1.541381265 x = -1.541381265 Simplifying x = -1.541381265Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.541381265, -1.541381265}Solution
x = {0, 4.541381265, -1.541381265}
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