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Simplifying 6x2 + -68x + 120 = 0 Reorder the terms: 120 + -68x + 6x2 = 0 Solving 120 + -68x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(60 + -34x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(60 + -34x + 3x2)' equal to zero and attempt to solve: Simplifying 60 + -34x + 3x2 = 0 Solving 60 + -34x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 20 + -11.33333333x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -11.33333333x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -11.33333333x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -11.33333333x + x2 = 0 + -20 -11.33333333x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -11.33333333x + x2 = -20 The x term is -11.33333333x. Take half its coefficient (-5.666666665). Square it (32.11111109) and add it to both sides. Add '32.11111109' to each side of the equation. -11.33333333x + 32.11111109 + x2 = -20 + 32.11111109 Reorder the terms: 32.11111109 + -11.33333333x + x2 = -20 + 32.11111109 Combine like terms: -20 + 32.11111109 = 12.11111109 32.11111109 + -11.33333333x + x2 = 12.11111109 Factor a perfect square on the left side: (x + -5.666666665)(x + -5.666666665) = 12.11111109 Calculate the square root of the right side: 3.480102167 Break this problem into two subproblems by setting (x + -5.666666665) equal to 3.480102167 and -3.480102167.Subproblem 1
x + -5.666666665 = 3.480102167 Simplifying x + -5.666666665 = 3.480102167 Reorder the terms: -5.666666665 + x = 3.480102167 Solving -5.666666665 + x = 3.480102167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.666666665' to each side of the equation. -5.666666665 + 5.666666665 + x = 3.480102167 + 5.666666665 Combine like terms: -5.666666665 + 5.666666665 = 0.000000000 0.000000000 + x = 3.480102167 + 5.666666665 x = 3.480102167 + 5.666666665 Combine like terms: 3.480102167 + 5.666666665 = 9.146768832 x = 9.146768832 Simplifying x = 9.146768832Subproblem 2
x + -5.666666665 = -3.480102167 Simplifying x + -5.666666665 = -3.480102167 Reorder the terms: -5.666666665 + x = -3.480102167 Solving -5.666666665 + x = -3.480102167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.666666665' to each side of the equation. -5.666666665 + 5.666666665 + x = -3.480102167 + 5.666666665 Combine like terms: -5.666666665 + 5.666666665 = 0.000000000 0.000000000 + x = -3.480102167 + 5.666666665 x = -3.480102167 + 5.666666665 Combine like terms: -3.480102167 + 5.666666665 = 2.186564498 x = 2.186564498 Simplifying x = 2.186564498Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.146768832, 2.186564498}Solution
x = {9.146768832, 2.186564498}
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