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Simplifying 2x3 + -20x2 + -40x = 0 Reorder the terms: -40x + -20x2 + 2x3 = 0 Solving -40x + -20x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-20 + -10x + 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 '(-20 + -10x + x2)' equal to zero and attempt to solve: Simplifying -20 + -10x + x2 = 0 Solving -20 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -10x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -10x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -10x + x2 = 0 + 20 -10x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -10x + x2 = 20 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 20 + 25 Reorder the terms: 25 + -10x + x2 = 20 + 25 Combine like terms: 20 + 25 = 45 25 + -10x + x2 = 45 Factor a perfect square on the left side: (x + -5)(x + -5) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + -5) equal to 6.708203933 and -6.708203933.Subproblem 1
x + -5 = 6.708203933 Simplifying x + -5 = 6.708203933 Reorder the terms: -5 + x = 6.708203933 Solving -5 + x = 6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 6.708203933 + 5 Combine like terms: -5 + 5 = 0 0 + x = 6.708203933 + 5 x = 6.708203933 + 5 Combine like terms: 6.708203933 + 5 = 11.708203933 x = 11.708203933 Simplifying x = 11.708203933Subproblem 2
x + -5 = -6.708203933 Simplifying x + -5 = -6.708203933 Reorder the terms: -5 + x = -6.708203933 Solving -5 + x = -6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -6.708203933 + 5 Combine like terms: -5 + 5 = 0 0 + x = -6.708203933 + 5 x = -6.708203933 + 5 Combine like terms: -6.708203933 + 5 = -1.708203933 x = -1.708203933 Simplifying x = -1.708203933Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.708203933, -1.708203933}Solution
x = {0, 11.708203933, -1.708203933}
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