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Simplifying 6(x + 8) + 4x(3x + -7) + -9(2x + 1) + 8 + -6x = 4(3x + 6) + -7(5x) + 9x + -7 Reorder the terms: 6(8 + x) + 4x(3x + -7) + -9(2x + 1) + 8 + -6x = 4(3x + 6) + -7(5x) + 9x + -7 (8 * 6 + x * 6) + 4x(3x + -7) + -9(2x + 1) + 8 + -6x = 4(3x + 6) + -7(5x) + 9x + -7 (48 + 6x) + 4x(3x + -7) + -9(2x + 1) + 8 + -6x = 4(3x + 6) + -7(5x) + 9x + -7 Reorder the terms: 48 + 6x + 4x(-7 + 3x) + -9(2x + 1) + 8 + -6x = 4(3x + 6) + -7(5x) + 9x + -7 48 + 6x + (-7 * 4x + 3x * 4x) + -9(2x + 1) + 8 + -6x = 4(3x + 6) + -7(5x) + 9x + -7 48 + 6x + (-28x + 12x2) + -9(2x + 1) + 8 + -6x = 4(3x + 6) + -7(5x) + 9x + -7 Reorder the terms: 48 + 6x + -28x + 12x2 + -9(1 + 2x) + 8 + -6x = 4(3x + 6) + -7(5x) + 9x + -7 48 + 6x + -28x + 12x2 + (1 * -9 + 2x * -9) + 8 + -6x = 4(3x + 6) + -7(5x) + 9x + -7 48 + 6x + -28x + 12x2 + (-9 + -18x) + 8 + -6x = 4(3x + 6) + -7(5x) + 9x + -7 Reorder the terms: 48 + -9 + 8 + 6x + -28x + -18x + -6x + 12x2 = 4(3x + 6) + -7(5x) + 9x + -7 Combine like terms: 48 + -9 = 39 39 + 8 + 6x + -28x + -18x + -6x + 12x2 = 4(3x + 6) + -7(5x) + 9x + -7 Combine like terms: 39 + 8 = 47 47 + 6x + -28x + -18x + -6x + 12x2 = 4(3x + 6) + -7(5x) + 9x + -7 Combine like terms: 6x + -28x = -22x 47 + -22x + -18x + -6x + 12x2 = 4(3x + 6) + -7(5x) + 9x + -7 Combine like terms: -22x + -18x = -40x 47 + -40x + -6x + 12x2 = 4(3x + 6) + -7(5x) + 9x + -7 Combine like terms: -40x + -6x = -46x 47 + -46x + 12x2 = 4(3x + 6) + -7(5x) + 9x + -7 Reorder the terms: 47 + -46x + 12x2 = 4(6 + 3x) + -7(5x) + 9x + -7 47 + -46x + 12x2 = (6 * 4 + 3x * 4) + -7(5x) + 9x + -7 47 + -46x + 12x2 = (24 + 12x) + -7(5x) + 9x + -7 Remove parenthesis around (5x) 47 + -46x + 12x2 = 24 + 12x + -7 * 5x + 9x + -7 Multiply -7 * 5 47 + -46x + 12x2 = 24 + 12x + -35x + 9x + -7 Reorder the terms: 47 + -46x + 12x2 = 24 + -7 + 12x + -35x + 9x Combine like terms: 24 + -7 = 17 47 + -46x + 12x2 = 17 + 12x + -35x + 9x Combine like terms: 12x + -35x = -23x 47 + -46x + 12x2 = 17 + -23x + 9x Combine like terms: -23x + 9x = -14x 47 + -46x + 12x2 = 17 + -14x Solving 47 + -46x + 12x2 = 17 + -14x Solving for variable 'x'. Reorder the terms: 47 + -17 + -46x + 14x + 12x2 = 17 + -14x + -17 + 14x Combine like terms: 47 + -17 = 30 30 + -46x + 14x + 12x2 = 17 + -14x + -17 + 14x Combine like terms: -46x + 14x = -32x 30 + -32x + 12x2 = 17 + -14x + -17 + 14x Reorder the terms: 30 + -32x + 12x2 = 17 + -17 + -14x + 14x Combine like terms: 17 + -17 = 0 30 + -32x + 12x2 = 0 + -14x + 14x 30 + -32x + 12x2 = -14x + 14x Combine like terms: -14x + 14x = 0 30 + -32x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(15 + -16x + 6x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + -16x + 6x2)' equal to zero and attempt to solve: Simplifying 15 + -16x + 6x2 = 0 Solving 15 + -16x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 2.5 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -2.666666667x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -2.666666667x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -2.666666667x + x2 = 0 + -2.5 -2.666666667x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -2.666666667x + x2 = -2.5 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = -2.5 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = -2.5 + 1.777777780 Combine like terms: -2.5 + 1.777777780 = -0.72222222 1.777777780 + -2.666666667x + x2 = -0.72222222 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = -0.72222222 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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