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Simplifying -3x(6x + 1) + -2x = 6 Reorder the terms: -3x(1 + 6x) + -2x = 6 (1 * -3x + 6x * -3x) + -2x = 6 (-3x + -18x2) + -2x = 6 Reorder the terms: -3x + -2x + -18x2 = 6 Combine like terms: -3x + -2x = -5x -5x + -18x2 = 6 Solving -5x + -18x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + -5x + -18x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -5x + -18x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 5x + 18x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 5x + 18x2)' equal to zero and attempt to solve: Simplifying 6 + 5x + 18x2 = 0 Solving 6 + 5x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.3333333333 + 0.2777777778x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 0.2777777778x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 0.2777777778x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 0.2777777778x + x2 = 0 + -0.3333333333 0.2777777778x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 0.2777777778x + x2 = -0.3333333333 The x term is 0.2777777778x. Take half its coefficient (0.1388888889). Square it (0.01929012346) and add it to both sides. Add '0.01929012346' to each side of the equation. 0.2777777778x + 0.01929012346 + x2 = -0.3333333333 + 0.01929012346 Reorder the terms: 0.01929012346 + 0.2777777778x + x2 = -0.3333333333 + 0.01929012346 Combine like terms: -0.3333333333 + 0.01929012346 = -0.31404320984 0.01929012346 + 0.2777777778x + x2 = -0.31404320984 Factor a perfect square on the left side: (x + 0.1388888889)(x + 0.1388888889) = -0.31404320984 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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