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Simplifying x3 + -57x2 + 96x = 0 Reorder the terms: 96x + -57x2 + x3 = 0 Solving 96x + -57x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(96 + -57x + 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 '(96 + -57x + x2)' equal to zero and attempt to solve: Simplifying 96 + -57x + x2 = 0 Solving 96 + -57x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-96' to each side of the equation. 96 + -57x + -96 + x2 = 0 + -96 Reorder the terms: 96 + -96 + -57x + x2 = 0 + -96 Combine like terms: 96 + -96 = 0 0 + -57x + x2 = 0 + -96 -57x + x2 = 0 + -96 Combine like terms: 0 + -96 = -96 -57x + x2 = -96 The x term is -57x. Take half its coefficient (-28.5). Square it (812.25) and add it to both sides. Add '812.25' to each side of the equation. -57x + 812.25 + x2 = -96 + 812.25 Reorder the terms: 812.25 + -57x + x2 = -96 + 812.25 Combine like terms: -96 + 812.25 = 716.25 812.25 + -57x + x2 = 716.25 Factor a perfect square on the left side: (x + -28.5)(x + -28.5) = 716.25 Calculate the square root of the right side: 26.762847382 Break this problem into two subproblems by setting (x + -28.5) equal to 26.762847382 and -26.762847382.Subproblem 1
x + -28.5 = 26.762847382 Simplifying x + -28.5 = 26.762847382 Reorder the terms: -28.5 + x = 26.762847382 Solving -28.5 + x = 26.762847382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.5' to each side of the equation. -28.5 + 28.5 + x = 26.762847382 + 28.5 Combine like terms: -28.5 + 28.5 = 0.0 0.0 + x = 26.762847382 + 28.5 x = 26.762847382 + 28.5 Combine like terms: 26.762847382 + 28.5 = 55.262847382 x = 55.262847382 Simplifying x = 55.262847382Subproblem 2
x + -28.5 = -26.762847382 Simplifying x + -28.5 = -26.762847382 Reorder the terms: -28.5 + x = -26.762847382 Solving -28.5 + x = -26.762847382 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28.5' to each side of the equation. -28.5 + 28.5 + x = -26.762847382 + 28.5 Combine like terms: -28.5 + 28.5 = 0.0 0.0 + x = -26.762847382 + 28.5 x = -26.762847382 + 28.5 Combine like terms: -26.762847382 + 28.5 = 1.737152618 x = 1.737152618 Simplifying x = 1.737152618Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.262847382, 1.737152618}Solution
x = {0, 55.262847382, 1.737152618}
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