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Simplifying x3 + -20x2 + 18x = 0 Reorder the terms: 18x + -20x2 + x3 = 0 Solving 18x + -20x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(18 + -20x + x2) = 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 '(18 + -20x + x2)' equal to zero and attempt to solve: Simplifying 18 + -20x + x2 = 0 Solving 18 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -20x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + -20x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -20x + x2 = 0 + -18 -20x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -20x + x2 = -18 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -18 + 100 Reorder the terms: 100 + -20x + x2 = -18 + 100 Combine like terms: -18 + 100 = 82 100 + -20x + x2 = 82 Factor a perfect square on the left side: (x + -10)(x + -10) = 82 Calculate the square root of the right side: 9.055385138 Break this problem into two subproblems by setting (x + -10) equal to 9.055385138 and -9.055385138.Subproblem 1
x + -10 = 9.055385138 Simplifying x + -10 = 9.055385138 Reorder the terms: -10 + x = 9.055385138 Solving -10 + x = 9.055385138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 9.055385138 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.055385138 + 10 x = 9.055385138 + 10 Combine like terms: 9.055385138 + 10 = 19.055385138 x = 19.055385138 Simplifying x = 19.055385138Subproblem 2
x + -10 = -9.055385138 Simplifying x + -10 = -9.055385138 Reorder the terms: -10 + x = -9.055385138 Solving -10 + x = -9.055385138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -9.055385138 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.055385138 + 10 x = -9.055385138 + 10 Combine like terms: -9.055385138 + 10 = 0.944614862 x = 0.944614862 Simplifying x = 0.944614862Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.055385138, 0.944614862}Solution
x = {0, 19.055385138, 0.944614862}
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