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Simplifying x * x * x + -36x = 9x * 9x Multiply x * x x2 * x + -36x = 9x * 9x Multiply x2 * x x3 + -36x = 9x * 9x Reorder the terms: -36x + x3 = 9x * 9x Reorder the terms for easier multiplication: -36x + x3 = 9 * 9x * x Multiply 9 * 9 -36x + x3 = 81x * x Multiply x * x -36x + x3 = 81x2 Solving -36x + x3 = 81x2 Solving for variable 'x'. Reorder the terms: -36x + -81x2 + x3 = 81x2 + -81x2 Combine like terms: 81x2 + -81x2 = 0 -36x + -81x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-36 + -81x + 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 '(-36 + -81x + x2)' equal to zero and attempt to solve: Simplifying -36 + -81x + x2 = 0 Solving -36 + -81x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -81x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -81x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -81x + x2 = 0 + 36 -81x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -81x + x2 = 36 The x term is -81x. Take half its coefficient (-40.5). Square it (1640.25) and add it to both sides. Add '1640.25' to each side of the equation. -81x + 1640.25 + x2 = 36 + 1640.25 Reorder the terms: 1640.25 + -81x + x2 = 36 + 1640.25 Combine like terms: 36 + 1640.25 = 1676.25 1640.25 + -81x + x2 = 1676.25 Factor a perfect square on the left side: (x + -40.5)(x + -40.5) = 1676.25 Calculate the square root of the right side: 40.942032192 Break this problem into two subproblems by setting (x + -40.5) equal to 40.942032192 and -40.942032192.Subproblem 1
x + -40.5 = 40.942032192 Simplifying x + -40.5 = 40.942032192 Reorder the terms: -40.5 + x = 40.942032192 Solving -40.5 + x = 40.942032192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.5' to each side of the equation. -40.5 + 40.5 + x = 40.942032192 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + x = 40.942032192 + 40.5 x = 40.942032192 + 40.5 Combine like terms: 40.942032192 + 40.5 = 81.442032192 x = 81.442032192 Simplifying x = 81.442032192Subproblem 2
x + -40.5 = -40.942032192 Simplifying x + -40.5 = -40.942032192 Reorder the terms: -40.5 + x = -40.942032192 Solving -40.5 + x = -40.942032192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.5' to each side of the equation. -40.5 + 40.5 + x = -40.942032192 + 40.5 Combine like terms: -40.5 + 40.5 = 0.0 0.0 + x = -40.942032192 + 40.5 x = -40.942032192 + 40.5 Combine like terms: -40.942032192 + 40.5 = -0.442032192 x = -0.442032192 Simplifying x = -0.442032192Solution
The solution to the problem is based on the solutions from the subproblems. x = {81.442032192, -0.442032192}Solution
x = {0, 81.442032192, -0.442032192}
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