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Simplifying -6x + -2 = (3x + 1) * 3x + 1 Reorder the terms: -2 + -6x = (3x + 1) * 3x + 1 Reorder the terms: -2 + -6x = (1 + 3x) * 3x + 1 Reorder the terms for easier multiplication: -2 + -6x = 3x(1 + 3x) + 1 -2 + -6x = (1 * 3x + 3x * 3x) + 1 -2 + -6x = (3x + 9x2) + 1 Reorder the terms: -2 + -6x = 1 + 3x + 9x2 Solving -2 + -6x = 1 + 3x + 9x2 Solving for variable 'x'. Reorder the terms: -2 + -1 + -6x + -3x + -9x2 = 1 + 3x + 9x2 + -1 + -3x + -9x2 Combine like terms: -2 + -1 = -3 -3 + -6x + -3x + -9x2 = 1 + 3x + 9x2 + -1 + -3x + -9x2 Combine like terms: -6x + -3x = -9x -3 + -9x + -9x2 = 1 + 3x + 9x2 + -1 + -3x + -9x2 Reorder the terms: -3 + -9x + -9x2 = 1 + -1 + 3x + -3x + 9x2 + -9x2 Combine like terms: 1 + -1 = 0 -3 + -9x + -9x2 = 0 + 3x + -3x + 9x2 + -9x2 -3 + -9x + -9x2 = 3x + -3x + 9x2 + -9x2 Combine like terms: 3x + -3x = 0 -3 + -9x + -9x2 = 0 + 9x2 + -9x2 -3 + -9x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -3 + -9x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(1 + 3x + 3x2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(1 + 3x + 3x2)' equal to zero and attempt to solve: Simplifying 1 + 3x + 3x2 = 0 Solving 1 + 3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.3333333333 + x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + x + x2 = 0 + -0.3333333333 x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 x + x2 = -0.3333333333 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 = -0.3333333333 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -0.3333333333 + 0.25 Combine like terms: -0.3333333333 + 0.25 = -0.0833333333 1.25 + x2 = -0.0833333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.0833333333 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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