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Simplifying (6x2 + -6x + -39) + (6x2 + 9x) = 0 Reorder the terms: (-39 + -6x + 6x2) + (6x2 + 9x) = 0 Remove parenthesis around (-39 + -6x + 6x2) -39 + -6x + 6x2 + (6x2 + 9x) = 0 Reorder the terms: -39 + -6x + 6x2 + (9x + 6x2) = 0 Remove parenthesis around (9x + 6x2) -39 + -6x + 6x2 + 9x + 6x2 = 0 Reorder the terms: -39 + -6x + 9x + 6x2 + 6x2 = 0 Combine like terms: -6x + 9x = 3x -39 + 3x + 6x2 + 6x2 = 0 Combine like terms: 6x2 + 6x2 = 12x2 -39 + 3x + 12x2 = 0 Solving -39 + 3x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-13 + x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-13 + x + 4x2)' equal to zero and attempt to solve: Simplifying -13 + x + 4x2 = 0 Solving -13 + x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.25 + 0.25x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + 0.25x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + 0.25x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + 0.25x + x2 = 0 + 3.25 0.25x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 0.25x + x2 = 3.25 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. 0.25x + 0.25 + x2 = 3.25 + 0.25 Reorder the terms: 0.25 + 0.25x + x2 = 3.25 + 0.25 Combine like terms: 3.25 + 0.25 = 3.5 0.25 + 0.25x + x2 = 3.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (x + 0.5) equal to 1.870828693 and -1.870828693.Subproblem 1
x + 0.5 = 1.870828693 Simplifying x + 0.5 = 1.870828693 Reorder the terms: 0.5 + x = 1.870828693 Solving 0.5 + x = 1.870828693 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 = 1.870828693 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.870828693 + -0.5 x = 1.870828693 + -0.5 Combine like terms: 1.870828693 + -0.5 = 1.370828693 x = 1.370828693 Simplifying x = 1.370828693Subproblem 2
x + 0.5 = -1.870828693 Simplifying x + 0.5 = -1.870828693 Reorder the terms: 0.5 + x = -1.870828693 Solving 0.5 + x = -1.870828693 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 = -1.870828693 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.870828693 + -0.5 x = -1.870828693 + -0.5 Combine like terms: -1.870828693 + -0.5 = -2.370828693 x = -2.370828693 Simplifying x = -2.370828693Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.370828693, -2.370828693}Solution
x = {1.370828693, -2.370828693}
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