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Simplifying 8x(6x + 4) = 16x + -2 Reorder the terms: 8x(4 + 6x) = 16x + -2 (4 * 8x + 6x * 8x) = 16x + -2 (32x + 48x2) = 16x + -2 Reorder the terms: 32x + 48x2 = -2 + 16x Solving 32x + 48x2 = -2 + 16x Solving for variable 'x'. Reorder the terms: 2 + 32x + -16x + 48x2 = -2 + 16x + 2 + -16x Combine like terms: 32x + -16x = 16x 2 + 16x + 48x2 = -2 + 16x + 2 + -16x Reorder the terms: 2 + 16x + 48x2 = -2 + 2 + 16x + -16x Combine like terms: -2 + 2 = 0 2 + 16x + 48x2 = 0 + 16x + -16x 2 + 16x + 48x2 = 16x + -16x Combine like terms: 16x + -16x = 0 2 + 16x + 48x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 8x + 24x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 8x + 24x2)' equal to zero and attempt to solve: Simplifying 1 + 8x + 24x2 = 0 Solving 1 + 8x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. 0.04166666667 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '-0.04166666667' to each side of the equation. 0.04166666667 + 0.3333333333x + -0.04166666667 + x2 = 0 + -0.04166666667 Reorder the terms: 0.04166666667 + -0.04166666667 + 0.3333333333x + x2 = 0 + -0.04166666667 Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000 0.00000000000 + 0.3333333333x + x2 = 0 + -0.04166666667 0.3333333333x + x2 = 0 + -0.04166666667 Combine like terms: 0 + -0.04166666667 = -0.04166666667 0.3333333333x + x2 = -0.04166666667 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = -0.04166666667 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = -0.04166666667 + 0.02777777779 Combine like terms: -0.04166666667 + 0.02777777779 = -0.01388888888 0.02777777779 + 0.3333333333x + x2 = -0.01388888888 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = -0.01388888888 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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