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Simplifying 6(-1 + -2x) = 8x(7x + 3) + 4 (-1 * 6 + -2x * 6) = 8x(7x + 3) + 4 (-6 + -12x) = 8x(7x + 3) + 4 Reorder the terms: -6 + -12x = 8x(3 + 7x) + 4 -6 + -12x = (3 * 8x + 7x * 8x) + 4 -6 + -12x = (24x + 56x2) + 4 Reorder the terms: -6 + -12x = 4 + 24x + 56x2 Solving -6 + -12x = 4 + 24x + 56x2 Solving for variable 'x'. Reorder the terms: -6 + -4 + -12x + -24x + -56x2 = 4 + 24x + 56x2 + -4 + -24x + -56x2 Combine like terms: -6 + -4 = -10 -10 + -12x + -24x + -56x2 = 4 + 24x + 56x2 + -4 + -24x + -56x2 Combine like terms: -12x + -24x = -36x -10 + -36x + -56x2 = 4 + 24x + 56x2 + -4 + -24x + -56x2 Reorder the terms: -10 + -36x + -56x2 = 4 + -4 + 24x + -24x + 56x2 + -56x2 Combine like terms: 4 + -4 = 0 -10 + -36x + -56x2 = 0 + 24x + -24x + 56x2 + -56x2 -10 + -36x + -56x2 = 24x + -24x + 56x2 + -56x2 Combine like terms: 24x + -24x = 0 -10 + -36x + -56x2 = 0 + 56x2 + -56x2 -10 + -36x + -56x2 = 56x2 + -56x2 Combine like terms: 56x2 + -56x2 = 0 -10 + -36x + -56x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(5 + 18x + 28x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(5 + 18x + 28x2)' equal to zero and attempt to solve: Simplifying 5 + 18x + 28x2 = 0 Solving 5 + 18x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. 0.1785714286 + 0.6428571429x + x2 = 0 Move the constant term to the right: Add '-0.1785714286' to each side of the equation. 0.1785714286 + 0.6428571429x + -0.1785714286 + x2 = 0 + -0.1785714286 Reorder the terms: 0.1785714286 + -0.1785714286 + 0.6428571429x + x2 = 0 + -0.1785714286 Combine like terms: 0.1785714286 + -0.1785714286 = 0.0000000000 0.0000000000 + 0.6428571429x + x2 = 0 + -0.1785714286 0.6428571429x + x2 = 0 + -0.1785714286 Combine like terms: 0 + -0.1785714286 = -0.1785714286 0.6428571429x + x2 = -0.1785714286 The x term is 0.6428571429x. Take half its coefficient (0.3214285715). Square it (0.1033163266) and add it to both sides. Add '0.1033163266' to each side of the equation. 0.6428571429x + 0.1033163266 + x2 = -0.1785714286 + 0.1033163266 Reorder the terms: 0.1033163266 + 0.6428571429x + x2 = -0.1785714286 + 0.1033163266 Combine like terms: -0.1785714286 + 0.1033163266 = -0.075255102 0.1033163266 + 0.6428571429x + x2 = -0.075255102 Factor a perfect square on the left side: (x + 0.3214285715)(x + 0.3214285715) = -0.075255102 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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