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Simplifying 0 = 6x2 + 6x + -8 Reorder the terms: 0 = -8 + 6x + 6x2 Solving 0 = -8 + 6x + 6x2 Solving for variable 'x'. Combine like terms: 0 + 8 = 8 8 + -6x + -6x2 = -8 + 6x + 6x2 + 8 + -6x + -6x2 Reorder the terms: 8 + -6x + -6x2 = -8 + 8 + 6x + -6x + 6x2 + -6x2 Combine like terms: -8 + 8 = 0 8 + -6x + -6x2 = 0 + 6x + -6x + 6x2 + -6x2 8 + -6x + -6x2 = 6x + -6x + 6x2 + -6x2 Combine like terms: 6x + -6x = 0 8 + -6x + -6x2 = 0 + 6x2 + -6x2 8 + -6x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 8 + -6x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -3x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -3x + -3x2)' equal to zero and attempt to solve: Simplifying 4 + -3x + -3x2 = 0 Solving 4 + -3x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1.333333333 + x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + x + x2 = 0 + 1.333333333 x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 x + x2 = 1.333333333 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 = 1.333333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 1.333333333 + 0.25 Combine like terms: 1.333333333 + 0.25 = 1.583333333 1.25 + x2 = 1.583333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.583333333 Calculate the square root of the right side: 1.258305739 Break this problem into two subproblems by setting (x + 0.5) equal to 1.258305739 and -1.258305739.Subproblem 1
x + 0.5 = 1.258305739 Simplifying x + 0.5 = 1.258305739 Reorder the terms: 0.5 + x = 1.258305739 Solving 0.5 + x = 1.258305739 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 = 1.258305739 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.258305739 + -0.5 x = 1.258305739 + -0.5 Combine like terms: 1.258305739 + -0.5 = 0.758305739 x = 0.758305739 Simplifying x = 0.758305739Subproblem 2
x + 0.5 = -1.258305739 Simplifying x + 0.5 = -1.258305739 Reorder the terms: 0.5 + x = -1.258305739 Solving 0.5 + x = -1.258305739 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 = -1.258305739 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.258305739 + -0.5 x = -1.258305739 + -0.5 Combine like terms: -1.258305739 + -0.5 = -1.758305739 x = -1.758305739 Simplifying x = -1.758305739Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.758305739, -1.758305739}Solution
x = {0.758305739, -1.758305739}
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