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Simplifying x3 + 3x2 + -144x = 0 Reorder the terms: -144x + 3x2 + x3 = 0 Solving -144x + 3x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-144 + 3x + 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 '(-144 + 3x + x2)' equal to zero and attempt to solve: Simplifying -144 + 3x + x2 = 0 Solving -144 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + 3x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + 3x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 3x + x2 = 0 + 144 3x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 3x + x2 = 144 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 144 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 144 + 2.25 Combine like terms: 144 + 2.25 = 146.25 2.25 + 3x + x2 = 146.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 146.25 Calculate the square root of the right side: 12.093386622 Break this problem into two subproblems by setting (x + 1.5) equal to 12.093386622 and -12.093386622.Subproblem 1
x + 1.5 = 12.093386622 Simplifying x + 1.5 = 12.093386622 Reorder the terms: 1.5 + x = 12.093386622 Solving 1.5 + x = 12.093386622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 12.093386622 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 12.093386622 + -1.5 x = 12.093386622 + -1.5 Combine like terms: 12.093386622 + -1.5 = 10.593386622 x = 10.593386622 Simplifying x = 10.593386622Subproblem 2
x + 1.5 = -12.093386622 Simplifying x + 1.5 = -12.093386622 Reorder the terms: 1.5 + x = -12.093386622 Solving 1.5 + x = -12.093386622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -12.093386622 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -12.093386622 + -1.5 x = -12.093386622 + -1.5 Combine like terms: -12.093386622 + -1.5 = -13.593386622 x = -13.593386622 Simplifying x = -13.593386622Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.593386622, -13.593386622}Solution
x = {0, 10.593386622, -13.593386622}
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