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Simplifying 2x3 + 12x2 + 11x = 0 Reorder the terms: 11x + 12x2 + 2x3 = 0 Solving 11x + 12x2 + 2x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(11 + 12x + 2x2) = 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 + 12x + 2x2)' equal to zero and attempt to solve: Simplifying 11 + 12x + 2x2 = 0 Solving 11 + 12x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5.5 + 6x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + 6x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + 6x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + 6x + x2 = 0 + -5.5 6x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 6x + x2 = -5.5 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -5.5 + 9 Reorder the terms: 9 + 6x + x2 = -5.5 + 9 Combine like terms: -5.5 + 9 = 3.5 9 + 6x + x2 = 3.5 Factor a perfect square on the left side: (x + 3)(x + 3) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (x + 3) equal to 1.870828693 and -1.870828693.Subproblem 1
x + 3 = 1.870828693 Simplifying x + 3 = 1.870828693 Reorder the terms: 3 + x = 1.870828693 Solving 3 + x = 1.870828693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 1.870828693 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1.870828693 + -3 x = 1.870828693 + -3 Combine like terms: 1.870828693 + -3 = -1.129171307 x = -1.129171307 Simplifying x = -1.129171307Subproblem 2
x + 3 = -1.870828693 Simplifying x + 3 = -1.870828693 Reorder the terms: 3 + x = -1.870828693 Solving 3 + x = -1.870828693 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -1.870828693 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1.870828693 + -3 x = -1.870828693 + -3 Combine like terms: -1.870828693 + -3 = -4.870828693 x = -4.870828693 Simplifying x = -4.870828693Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.129171307, -4.870828693}Solution
x = {0, -1.129171307, -4.870828693}
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