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Simplifying 0 = x3 + -2x2 + -11x Reorder the terms: 0 = -11x + -2x2 + x3 Solving 0 = -11x + -2x2 + x3 Solving for variable 'x'. Remove the zero: 11x + 2x2 + -1x3 = -11x + -2x2 + x3 + 11x + 2x2 + -1x3 Reorder the terms: 11x + 2x2 + -1x3 = -11x + 11x + -2x2 + 2x2 + x3 + -1x3 Combine like terms: -11x + 11x = 0 11x + 2x2 + -1x3 = 0 + -2x2 + 2x2 + x3 + -1x3 11x + 2x2 + -1x3 = -2x2 + 2x2 + x3 + -1x3 Combine like terms: -2x2 + 2x2 = 0 11x + 2x2 + -1x3 = 0 + x3 + -1x3 11x + 2x2 + -1x3 = x3 + -1x3 Combine like terms: x3 + -1x3 = 0 11x + 2x2 + -1x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(11 + 2x + -1x2) = 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 '(11 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying 11 + 2x + -1x2 = 0 Solving 11 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -11 + -2x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -2x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -2x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -2x + x2 = 0 + 11 -2x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -2x + x2 = 11 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 = 11 + 1 Reorder the terms: 1 + -2x + x2 = 11 + 1 Combine like terms: 11 + 1 = 12 1 + -2x + x2 = 12 Factor a perfect square on the left side: (x + -1)(x + -1) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (x + -1) equal to 3.464101615 and -3.464101615.Subproblem 1
x + -1 = 3.464101615 Simplifying x + -1 = 3.464101615 Reorder the terms: -1 + x = 3.464101615 Solving -1 + x = 3.464101615 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 = 3.464101615 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.464101615 + 1 x = 3.464101615 + 1 Combine like terms: 3.464101615 + 1 = 4.464101615 x = 4.464101615 Simplifying x = 4.464101615Subproblem 2
x + -1 = -3.464101615 Simplifying x + -1 = -3.464101615 Reorder the terms: -1 + x = -3.464101615 Solving -1 + x = -3.464101615 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 = -3.464101615 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.464101615 + 1 x = -3.464101615 + 1 Combine like terms: -3.464101615 + 1 = -2.464101615 x = -2.464101615 Simplifying x = -2.464101615Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.464101615, -2.464101615}Solution
x = {0, 4.464101615, -2.464101615}
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