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Simplifying 3x + -6 = 1x(7 + -6x) + -14 Reorder the terms: -6 + 3x = 1x(7 + -6x) + -14 -6 + 3x = (7 * 1x + -6x * 1x) + -14 -6 + 3x = (7x + -6x2) + -14 Reorder the terms: -6 + 3x = -14 + 7x + -6x2 Solving -6 + 3x = -14 + 7x + -6x2 Solving for variable 'x'. Reorder the terms: -6 + 14 + 3x + -7x + 6x2 = -14 + 7x + -6x2 + 14 + -7x + 6x2 Combine like terms: -6 + 14 = 8 8 + 3x + -7x + 6x2 = -14 + 7x + -6x2 + 14 + -7x + 6x2 Combine like terms: 3x + -7x = -4x 8 + -4x + 6x2 = -14 + 7x + -6x2 + 14 + -7x + 6x2 Reorder the terms: 8 + -4x + 6x2 = -14 + 14 + 7x + -7x + -6x2 + 6x2 Combine like terms: -14 + 14 = 0 8 + -4x + 6x2 = 0 + 7x + -7x + -6x2 + 6x2 8 + -4x + 6x2 = 7x + -7x + -6x2 + 6x2 Combine like terms: 7x + -7x = 0 8 + -4x + 6x2 = 0 + -6x2 + 6x2 8 + -4x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 8 + -4x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -2x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -2x + 3x2)' equal to zero and attempt to solve: Simplifying 4 + -2x + 3x2 = 0 Solving 4 + -2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -0.6666666667x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -0.6666666667x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -0.6666666667x + x2 = 0 + -1.333333333 -0.6666666667x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -0.6666666667x + x2 = -1.333333333 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = -1.333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = -1.333333333 + 0.1111111112 Combine like terms: -1.333333333 + 0.1111111112 = -1.2222222218 0.1111111112 + -0.6666666667x + x2 = -1.2222222218 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = -1.2222222218 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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