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Simplifying 2[x3 + -12x2 + -20x] = 0 Reorder the terms: 2[-20x + -12x2 + x3] = 0 [-20x * 2 + -12x2 * 2 + x3 * 2] = 0 [-40x + -24x2 + 2x3] = 0 Solving -40x + -24x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-20 + -12x + 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 + -12x + x2)' equal to zero and attempt to solve: Simplifying -20 + -12x + x2 = 0 Solving -20 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -12x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -12x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -12x + x2 = 0 + 20 -12x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -12x + x2 = 20 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 20 + 36 Reorder the terms: 36 + -12x + x2 = 20 + 36 Combine like terms: 20 + 36 = 56 36 + -12x + x2 = 56 Factor a perfect square on the left side: (x + -6)(x + -6) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (x + -6) equal to 7.483314774 and -7.483314774.Subproblem 1
x + -6 = 7.483314774 Simplifying x + -6 = 7.483314774 Reorder the terms: -6 + x = 7.483314774 Solving -6 + x = 7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 7.483314774 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.483314774 + 6 x = 7.483314774 + 6 Combine like terms: 7.483314774 + 6 = 13.483314774 x = 13.483314774 Simplifying x = 13.483314774Subproblem 2
x + -6 = -7.483314774 Simplifying x + -6 = -7.483314774 Reorder the terms: -6 + x = -7.483314774 Solving -6 + x = -7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -7.483314774 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.483314774 + 6 x = -7.483314774 + 6 Combine like terms: -7.483314774 + 6 = -1.483314774 x = -1.483314774 Simplifying x = -1.483314774Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.483314774, -1.483314774}Solution
x = {0, 13.483314774, -1.483314774}
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