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Simplifying 15 + -1(12x + 3)(27x + -3) = 75 + -18x Reorder the terms: 15 + -1(3 + 12x)(27x + -3) = 75 + -18x Reorder the terms: 15 + -1(3 + 12x)(-3 + 27x) = 75 + -18x Multiply (3 + 12x) * (-3 + 27x) 15 + -1(3(-3 + 27x) + 12x * (-3 + 27x)) = 75 + -18x 15 + -1((-3 * 3 + 27x * 3) + 12x * (-3 + 27x)) = 75 + -18x 15 + -1((-9 + 81x) + 12x * (-3 + 27x)) = 75 + -18x 15 + -1(-9 + 81x + (-3 * 12x + 27x * 12x)) = 75 + -18x 15 + -1(-9 + 81x + (-36x + 324x2)) = 75 + -18x Combine like terms: 81x + -36x = 45x 15 + -1(-9 + 45x + 324x2) = 75 + -18x 15 + (-9 * -1 + 45x * -1 + 324x2 * -1) = 75 + -18x 15 + (9 + -45x + -324x2) = 75 + -18x Combine like terms: 15 + 9 = 24 24 + -45x + -324x2 = 75 + -18x Solving 24 + -45x + -324x2 = 75 + -18x Solving for variable 'x'. Reorder the terms: 24 + -75 + -45x + 18x + -324x2 = 75 + -18x + -75 + 18x Combine like terms: 24 + -75 = -51 -51 + -45x + 18x + -324x2 = 75 + -18x + -75 + 18x Combine like terms: -45x + 18x = -27x -51 + -27x + -324x2 = 75 + -18x + -75 + 18x Reorder the terms: -51 + -27x + -324x2 = 75 + -75 + -18x + 18x Combine like terms: 75 + -75 = 0 -51 + -27x + -324x2 = 0 + -18x + 18x -51 + -27x + -324x2 = -18x + 18x Combine like terms: -18x + 18x = 0 -51 + -27x + -324x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(17 + 9x + 108x2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(17 + 9x + 108x2)' equal to zero and attempt to solve: Simplifying 17 + 9x + 108x2 = 0 Solving 17 + 9x + 108x2 = 0 Begin completing the square. Divide all terms by 108 the coefficient of the squared term: Divide each side by '108'. 0.1574074074 + 0.08333333333x + x2 = 0 Move the constant term to the right: Add '-0.1574074074' to each side of the equation. 0.1574074074 + 0.08333333333x + -0.1574074074 + x2 = 0 + -0.1574074074 Reorder the terms: 0.1574074074 + -0.1574074074 + 0.08333333333x + x2 = 0 + -0.1574074074 Combine like terms: 0.1574074074 + -0.1574074074 = 0.0000000000 0.0000000000 + 0.08333333333x + x2 = 0 + -0.1574074074 0.08333333333x + x2 = 0 + -0.1574074074 Combine like terms: 0 + -0.1574074074 = -0.1574074074 0.08333333333x + x2 = -0.1574074074 The x term is 0.08333333333x. Take half its coefficient (0.04166666667). Square it (0.001736111111) and add it to both sides. Add '0.001736111111' to each side of the equation. 0.08333333333x + 0.001736111111 + x2 = -0.1574074074 + 0.001736111111 Reorder the terms: 0.001736111111 + 0.08333333333x + x2 = -0.1574074074 + 0.001736111111 Combine like terms: -0.1574074074 + 0.001736111111 = -0.155671296289 0.001736111111 + 0.08333333333x + x2 = -0.155671296289 Factor a perfect square on the left side: (x + 0.04166666667)(x + 0.04166666667) = -0.155671296289 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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