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Simplifying 6x2 = 254 + -6x Solving 6x2 = 254 + -6x Solving for variable 'x'. Reorder the terms: -254 + 6x + 6x2 = 254 + -6x + -254 + 6x Reorder the terms: -254 + 6x + 6x2 = 254 + -254 + -6x + 6x Combine like terms: 254 + -254 = 0 -254 + 6x + 6x2 = 0 + -6x + 6x -254 + 6x + 6x2 = -6x + 6x Combine like terms: -6x + 6x = 0 -254 + 6x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-127 + 3x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-127 + 3x + 3x2)' equal to zero and attempt to solve: Simplifying -127 + 3x + 3x2 = 0 Solving -127 + 3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -42.33333333 + x + x2 = 0 Move the constant term to the right: Add '42.33333333' to each side of the equation. -42.33333333 + x + 42.33333333 + x2 = 0 + 42.33333333 Reorder the terms: -42.33333333 + 42.33333333 + x + x2 = 0 + 42.33333333 Combine like terms: -42.33333333 + 42.33333333 = 0.00000000 0.00000000 + x + x2 = 0 + 42.33333333 x + x2 = 0 + 42.33333333 Combine like terms: 0 + 42.33333333 = 42.33333333 x + x2 = 42.33333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 42.33333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 42.33333333 + 0.25 Combine like terms: 42.33333333 + 0.25 = 42.58333333 1.25 + x2 = 42.58333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 42.58333333 Calculate the square root of the right side: 6.52559065 Break this problem into two subproblems by setting (x + 0.5) equal to 6.52559065 and -6.52559065.Subproblem 1
x + 0.5 = 6.52559065 Simplifying x + 0.5 = 6.52559065 Reorder the terms: 0.5 + x = 6.52559065 Solving 0.5 + x = 6.52559065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 6.52559065 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.52559065 + -0.5 x = 6.52559065 + -0.5 Combine like terms: 6.52559065 + -0.5 = 6.02559065 x = 6.02559065 Simplifying x = 6.02559065Subproblem 2
x + 0.5 = -6.52559065 Simplifying x + 0.5 = -6.52559065 Reorder the terms: 0.5 + x = -6.52559065 Solving 0.5 + x = -6.52559065 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -6.52559065 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.52559065 + -0.5 x = -6.52559065 + -0.5 Combine like terms: -6.52559065 + -0.5 = -7.02559065 x = -7.02559065 Simplifying x = -7.02559065Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.02559065, -7.02559065}Solution
x = {6.02559065, -7.02559065}
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