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Simplifying 6x3 + 18x2 + -240x = 6x(x + -9) Reorder the terms: -240x + 18x2 + 6x3 = 6x(x + -9) Reorder the terms: -240x + 18x2 + 6x3 = 6x(-9 + x) -240x + 18x2 + 6x3 = (-9 * 6x + x * 6x) -240x + 18x2 + 6x3 = (-54x + 6x2) Solving -240x + 18x2 + 6x3 = -54x + 6x2 Solving for variable 'x'. Reorder the terms: -240x + 54x + 18x2 + -6x2 + 6x3 = -54x + 6x2 + 54x + -6x2 Combine like terms: -240x + 54x = -186x -186x + 18x2 + -6x2 + 6x3 = -54x + 6x2 + 54x + -6x2 Combine like terms: 18x2 + -6x2 = 12x2 -186x + 12x2 + 6x3 = -54x + 6x2 + 54x + -6x2 Reorder the terms: -186x + 12x2 + 6x3 = -54x + 54x + 6x2 + -6x2 Combine like terms: -54x + 54x = 0 -186x + 12x2 + 6x3 = 0 + 6x2 + -6x2 -186x + 12x2 + 6x3 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -186x + 12x2 + 6x3 = 0 Factor out the Greatest Common Factor (GCF), '6x'. 6x(-31 + 2x + x2) = 0 Ignore the factor 6.Subproblem 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 '(-31 + 2x + x2)' equal to zero and attempt to solve: Simplifying -31 + 2x + x2 = 0 Solving -31 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + 2x + 31 + x2 = 0 + 31 Reorder the terms: -31 + 31 + 2x + x2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 2x + x2 = 0 + 31 2x + x2 = 0 + 31 Combine like terms: 0 + 31 = 31 2x + x2 = 31 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 31 + 1 Reorder the terms: 1 + 2x + x2 = 31 + 1 Combine like terms: 31 + 1 = 32 1 + 2x + x2 = 32 Factor a perfect square on the left side: (x + 1)(x + 1) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + 1) equal to 5.656854249 and -5.656854249.Subproblem 1
x + 1 = 5.656854249 Simplifying x + 1 = 5.656854249 Reorder the terms: 1 + x = 5.656854249 Solving 1 + x = 5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 5.656854249 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.656854249 + -1 x = 5.656854249 + -1 Combine like terms: 5.656854249 + -1 = 4.656854249 x = 4.656854249 Simplifying x = 4.656854249Subproblem 2
x + 1 = -5.656854249 Simplifying x + 1 = -5.656854249 Reorder the terms: 1 + x = -5.656854249 Solving 1 + x = -5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -5.656854249 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.656854249 + -1 x = -5.656854249 + -1 Combine like terms: -5.656854249 + -1 = -6.656854249 x = -6.656854249 Simplifying x = -6.656854249Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.656854249, -6.656854249}Solution
x = {0, 4.656854249, -6.656854249}
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