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Simplifying 0 = x3 + -18x2 + 60x Reorder the terms: 0 = 60x + -18x2 + x3 Solving 0 = 60x + -18x2 + x3 Solving for variable 'x'. Remove the zero: -60x + 18x2 + -1x3 = 60x + -18x2 + x3 + -60x + 18x2 + -1x3 Reorder the terms: -60x + 18x2 + -1x3 = 60x + -60x + -18x2 + 18x2 + x3 + -1x3 Combine like terms: 60x + -60x = 0 -60x + 18x2 + -1x3 = 0 + -18x2 + 18x2 + x3 + -1x3 -60x + 18x2 + -1x3 = -18x2 + 18x2 + x3 + -1x3 Combine like terms: -18x2 + 18x2 = 0 -60x + 18x2 + -1x3 = 0 + x3 + -1x3 -60x + 18x2 + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 -60x + 18x2 + -1x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-60 + 18x + -1x2) = 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 '(-60 + 18x + -1x2)' equal to zero and attempt to solve: Simplifying -60 + 18x + -1x2 = 0 Solving -60 + 18x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 60 + -18x + x2 = 0 Move the constant term to the right: Add '-60' to each side of the equation. 60 + -18x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + -18x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -18x + x2 = 0 + -60 -18x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 -18x + x2 = -60 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -60 + 81 Reorder the terms: 81 + -18x + x2 = -60 + 81 Combine like terms: -60 + 81 = 21 81 + -18x + x2 = 21 Factor a perfect square on the left side: (x + -9)(x + -9) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x + -9) equal to 4.582575695 and -4.582575695.Subproblem 1
x + -9 = 4.582575695 Simplifying x + -9 = 4.582575695 Reorder the terms: -9 + x = 4.582575695 Solving -9 + x = 4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 4.582575695 + 9 Combine like terms: -9 + 9 = 0 0 + x = 4.582575695 + 9 x = 4.582575695 + 9 Combine like terms: 4.582575695 + 9 = 13.582575695 x = 13.582575695 Simplifying x = 13.582575695Subproblem 2
x + -9 = -4.582575695 Simplifying x + -9 = -4.582575695 Reorder the terms: -9 + x = -4.582575695 Solving -9 + x = -4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -4.582575695 + 9 Combine like terms: -9 + 9 = 0 0 + x = -4.582575695 + 9 x = -4.582575695 + 9 Combine like terms: -4.582575695 + 9 = 4.417424305 x = 4.417424305 Simplifying x = 4.417424305Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.582575695, 4.417424305}Solution
x = {0, 13.582575695, 4.417424305}
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