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Simplifying x2 + -11x2 + -186x + 1080 = 0 Reorder the terms: 1080 + -186x + x2 + -11x2 = 0 Combine like terms: x2 + -11x2 = -10x2 1080 + -186x + -10x2 = 0 Solving 1080 + -186x + -10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(540 + -93x + -5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(540 + -93x + -5x2)' equal to zero and attempt to solve: Simplifying 540 + -93x + -5x2 = 0 Solving 540 + -93x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -108 + 18.6x + x2 = 0 Move the constant term to the right: Add '108' to each side of the equation. -108 + 18.6x + 108 + x2 = 0 + 108 Reorder the terms: -108 + 108 + 18.6x + x2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + 18.6x + x2 = 0 + 108 18.6x + x2 = 0 + 108 Combine like terms: 0 + 108 = 108 18.6x + x2 = 108 The x term is 18.6x. Take half its coefficient (9.3). Square it (86.49) and add it to both sides. Add '86.49' to each side of the equation. 18.6x + 86.49 + x2 = 108 + 86.49 Reorder the terms: 86.49 + 18.6x + x2 = 108 + 86.49 Combine like terms: 108 + 86.49 = 194.49 86.49 + 18.6x + x2 = 194.49 Factor a perfect square on the left side: (x + 9.3)(x + 9.3) = 194.49 Calculate the square root of the right side: 13.945967159 Break this problem into two subproblems by setting (x + 9.3) equal to 13.945967159 and -13.945967159.Subproblem 1
x + 9.3 = 13.945967159 Simplifying x + 9.3 = 13.945967159 Reorder the terms: 9.3 + x = 13.945967159 Solving 9.3 + x = 13.945967159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.3' to each side of the equation. 9.3 + -9.3 + x = 13.945967159 + -9.3 Combine like terms: 9.3 + -9.3 = 0.0 0.0 + x = 13.945967159 + -9.3 x = 13.945967159 + -9.3 Combine like terms: 13.945967159 + -9.3 = 4.645967159 x = 4.645967159 Simplifying x = 4.645967159Subproblem 2
x + 9.3 = -13.945967159 Simplifying x + 9.3 = -13.945967159 Reorder the terms: 9.3 + x = -13.945967159 Solving 9.3 + x = -13.945967159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.3' to each side of the equation. 9.3 + -9.3 + x = -13.945967159 + -9.3 Combine like terms: 9.3 + -9.3 = 0.0 0.0 + x = -13.945967159 + -9.3 x = -13.945967159 + -9.3 Combine like terms: -13.945967159 + -9.3 = -23.245967159 x = -23.245967159 Simplifying x = -23.245967159Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.645967159, -23.245967159}Solution
x = {4.645967159, -23.245967159}
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