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Simplifying 0 = 42X + 18X2 + -2X3 Solving 0 = 42X + 18X2 + -2X3 Solving for variable 'X'. Remove the zero: -42X + -18X2 + 2X3 = 42X + 18X2 + -2X3 + -42X + -18X2 + 2X3 Reorder the terms: -42X + -18X2 + 2X3 = 42X + -42X + 18X2 + -18X2 + -2X3 + 2X3 Combine like terms: 42X + -42X = 0 -42X + -18X2 + 2X3 = 0 + 18X2 + -18X2 + -2X3 + 2X3 -42X + -18X2 + 2X3 = 18X2 + -18X2 + -2X3 + 2X3 Combine like terms: 18X2 + -18X2 = 0 -42X + -18X2 + 2X3 = 0 + -2X3 + 2X3 -42X + -18X2 + 2X3 = -2X3 + 2X3 Combine like terms: -2X3 + 2X3 = 0 -42X + -18X2 + 2X3 = 0 Factor out the Greatest Common Factor (GCF), '2X'. 2X(-21 + -9X + 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 '(-21 + -9X + X2)' equal to zero and attempt to solve: Simplifying -21 + -9X + X2 = 0 Solving -21 + -9X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -9X + 21 + X2 = 0 + 21 Reorder the terms: -21 + 21 + -9X + X2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -9X + X2 = 0 + 21 -9X + X2 = 0 + 21 Combine like terms: 0 + 21 = 21 -9X + X2 = 21 The X term is -9X. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9X + 20.25 + X2 = 21 + 20.25 Reorder the terms: 20.25 + -9X + X2 = 21 + 20.25 Combine like terms: 21 + 20.25 = 41.25 20.25 + -9X + X2 = 41.25 Factor a perfect square on the left side: (X + -4.5)(X + -4.5) = 41.25 Calculate the square root of the right side: 6.422616289 Break this problem into two subproblems by setting (X + -4.5) equal to 6.422616289 and -6.422616289.Subproblem 1
X + -4.5 = 6.422616289 Simplifying X + -4.5 = 6.422616289 Reorder the terms: -4.5 + X = 6.422616289 Solving -4.5 + X = 6.422616289 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + X = 6.422616289 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + X = 6.422616289 + 4.5 X = 6.422616289 + 4.5 Combine like terms: 6.422616289 + 4.5 = 10.922616289 X = 10.922616289 Simplifying X = 10.922616289Subproblem 2
X + -4.5 = -6.422616289 Simplifying X + -4.5 = -6.422616289 Reorder the terms: -4.5 + X = -6.422616289 Solving -4.5 + X = -6.422616289 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + X = -6.422616289 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + X = -6.422616289 + 4.5 X = -6.422616289 + 4.5 Combine like terms: -6.422616289 + 4.5 = -1.922616289 X = -1.922616289 Simplifying X = -1.922616289Solution
The solution to the problem is based on the solutions from the subproblems. X = {10.922616289, -1.922616289}Solution
X = {0, 10.922616289, -1.922616289}
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