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Simplifying 3X3 + 6X2 = 40X Reorder the terms: 6X2 + 3X3 = 40X Solving 6X2 + 3X3 = 40X Solving for variable 'X'. Reorder the terms: -40X + 6X2 + 3X3 = 40X + -40X Combine like terms: 40X + -40X = 0 -40X + 6X2 + 3X3 = 0 Factor out the Greatest Common Factor (GCF), 'X'. X(-40 + 6X + 3X2) = 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 '(-40 + 6X + 3X2)' equal to zero and attempt to solve: Simplifying -40 + 6X + 3X2 = 0 Solving -40 + 6X + 3X2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -13.33333333 + 2X + X2 = 0 Move the constant term to the right: Add '13.33333333' to each side of the equation. -13.33333333 + 2X + 13.33333333 + X2 = 0 + 13.33333333 Reorder the terms: -13.33333333 + 13.33333333 + 2X + X2 = 0 + 13.33333333 Combine like terms: -13.33333333 + 13.33333333 = 0.00000000 0.00000000 + 2X + X2 = 0 + 13.33333333 2X + X2 = 0 + 13.33333333 Combine like terms: 0 + 13.33333333 = 13.33333333 2X + X2 = 13.33333333 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 = 13.33333333 + 1 Reorder the terms: 1 + 2X + X2 = 13.33333333 + 1 Combine like terms: 13.33333333 + 1 = 14.33333333 1 + 2X + X2 = 14.33333333 Factor a perfect square on the left side: (X + 1)(X + 1) = 14.33333333 Calculate the square root of the right side: 3.785938897 Break this problem into two subproblems by setting (X + 1) equal to 3.785938897 and -3.785938897.Subproblem 1
X + 1 = 3.785938897 Simplifying X + 1 = 3.785938897 Reorder the terms: 1 + X = 3.785938897 Solving 1 + X = 3.785938897 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 = 3.785938897 + -1 Combine like terms: 1 + -1 = 0 0 + X = 3.785938897 + -1 X = 3.785938897 + -1 Combine like terms: 3.785938897 + -1 = 2.785938897 X = 2.785938897 Simplifying X = 2.785938897Subproblem 2
X + 1 = -3.785938897 Simplifying X + 1 = -3.785938897 Reorder the terms: 1 + X = -3.785938897 Solving 1 + X = -3.785938897 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 = -3.785938897 + -1 Combine like terms: 1 + -1 = 0 0 + X = -3.785938897 + -1 X = -3.785938897 + -1 Combine like terms: -3.785938897 + -1 = -4.785938897 X = -4.785938897 Simplifying X = -4.785938897Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.785938897, -4.785938897}Solution
X = {0, 2.785938897, -4.785938897}
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