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Simplifying 2x3 + -8x2 + -24x = 2x Reorder the terms: -24x + -8x2 + 2x3 = 2x Solving -24x + -8x2 + 2x3 = 2x Solving for variable 'x'. Reorder the terms: -24x + -2x + -8x2 + 2x3 = 2x + -2x Combine like terms: -24x + -2x = -26x -26x + -8x2 + 2x3 = 2x + -2x Combine like terms: 2x + -2x = 0 -26x + -8x2 + 2x3 = 0 Factor out the Greatest Common Factor (GCF), '2x'. 2x(-13 + -4x + x2) = 0 Ignore the factor 2.Subproblem 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 '(-13 + -4x + x2)' equal to zero and attempt to solve: Simplifying -13 + -4x + x2 = 0 Solving -13 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -4x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + -4x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -4x + x2 = 0 + 13 -4x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 -4x + x2 = 13 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 13 + 4 Reorder the terms: 4 + -4x + x2 = 13 + 4 Combine like terms: 13 + 4 = 17 4 + -4x + x2 = 17 Factor a perfect square on the left side: (x + -2)(x + -2) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x + -2) equal to 4.123105626 and -4.123105626.Subproblem 1
x + -2 = 4.123105626 Simplifying x + -2 = 4.123105626 Reorder the terms: -2 + x = 4.123105626 Solving -2 + x = 4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 4.123105626 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4.123105626 + 2 x = 4.123105626 + 2 Combine like terms: 4.123105626 + 2 = 6.123105626 x = 6.123105626 Simplifying x = 6.123105626Subproblem 2
x + -2 = -4.123105626 Simplifying x + -2 = -4.123105626 Reorder the terms: -2 + x = -4.123105626 Solving -2 + x = -4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -4.123105626 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4.123105626 + 2 x = -4.123105626 + 2 Combine like terms: -4.123105626 + 2 = -2.123105626 x = -2.123105626 Simplifying x = -2.123105626Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.123105626, -2.123105626}Solution
x = {0, 6.123105626, -2.123105626}
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