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Simplifying 6[-6x + 6 + 4x(x + 1)] = 6x + 2 Reorder the terms: 6[-6x + 6 + 4x(1 + x)] = 6x + 2 6[-6x + 6 + (1 * 4x + x * 4x)] = 6x + 2 6[-6x + 6 + (4x + 4x2)] = 6x + 2 Reorder the terms: 6[6 + -6x + 4x + 4x2] = 6x + 2 Combine like terms: -6x + 4x = -2x 6[6 + -2x + 4x2] = 6x + 2 [6 * 6 + -2x * 6 + 4x2 * 6] = 6x + 2 [36 + -12x + 24x2] = 6x + 2 Reorder the terms: 36 + -12x + 24x2 = 2 + 6x Solving 36 + -12x + 24x2 = 2 + 6x Solving for variable 'x'. Reorder the terms: 36 + -2 + -12x + -6x + 24x2 = 2 + 6x + -2 + -6x Combine like terms: 36 + -2 = 34 34 + -12x + -6x + 24x2 = 2 + 6x + -2 + -6x Combine like terms: -12x + -6x = -18x 34 + -18x + 24x2 = 2 + 6x + -2 + -6x Reorder the terms: 34 + -18x + 24x2 = 2 + -2 + 6x + -6x Combine like terms: 2 + -2 = 0 34 + -18x + 24x2 = 0 + 6x + -6x 34 + -18x + 24x2 = 6x + -6x Combine like terms: 6x + -6x = 0 34 + -18x + 24x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(17 + -9x + 12x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(17 + -9x + 12x2)' equal to zero and attempt to solve: Simplifying 17 + -9x + 12x2 = 0 Solving 17 + -9x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 1.416666667 + -0.75x + x2 = 0 Move the constant term to the right: Add '-1.416666667' to each side of the equation. 1.416666667 + -0.75x + -1.416666667 + x2 = 0 + -1.416666667 Reorder the terms: 1.416666667 + -1.416666667 + -0.75x + x2 = 0 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + -0.75x + x2 = 0 + -1.416666667 -0.75x + x2 = 0 + -1.416666667 Combine like terms: 0 + -1.416666667 = -1.416666667 -0.75x + x2 = -1.416666667 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = -1.416666667 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = -1.416666667 + 0.140625 Combine like terms: -1.416666667 + 0.140625 = -1.276041667 0.140625 + -0.75x + x2 = -1.276041667 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = -1.276041667 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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