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Simplifying 2a + -5 = 4(a + 1) * 9a + 5 Reorder the terms: -5 + 2a = 4(a + 1) * 9a + 5 Reorder the terms: -5 + 2a = 4(1 + a) * 9a + 5 Reorder the terms for easier multiplication: -5 + 2a = 4 * 9a(1 + a) + 5 Multiply 4 * 9 -5 + 2a = 36a(1 + a) + 5 -5 + 2a = (1 * 36a + a * 36a) + 5 -5 + 2a = (36a + 36a2) + 5 Reorder the terms: -5 + 2a = 5 + 36a + 36a2 Solving -5 + 2a = 5 + 36a + 36a2 Solving for variable 'a'. Reorder the terms: -5 + -5 + 2a + -36a + -36a2 = 5 + 36a + 36a2 + -5 + -36a + -36a2 Combine like terms: -5 + -5 = -10 -10 + 2a + -36a + -36a2 = 5 + 36a + 36a2 + -5 + -36a + -36a2 Combine like terms: 2a + -36a = -34a -10 + -34a + -36a2 = 5 + 36a + 36a2 + -5 + -36a + -36a2 Reorder the terms: -10 + -34a + -36a2 = 5 + -5 + 36a + -36a + 36a2 + -36a2 Combine like terms: 5 + -5 = 0 -10 + -34a + -36a2 = 0 + 36a + -36a + 36a2 + -36a2 -10 + -34a + -36a2 = 36a + -36a + 36a2 + -36a2 Combine like terms: 36a + -36a = 0 -10 + -34a + -36a2 = 0 + 36a2 + -36a2 -10 + -34a + -36a2 = 36a2 + -36a2 Combine like terms: 36a2 + -36a2 = 0 -10 + -34a + -36a2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(5 + 17a + 18a2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(5 + 17a + 18a2)' equal to zero and attempt to solve: Simplifying 5 + 17a + 18a2 = 0 Solving 5 + 17a + 18a2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.2777777778 + 0.9444444444a + a2 = 0 Move the constant term to the right: Add '-0.2777777778' to each side of the equation. 0.2777777778 + 0.9444444444a + -0.2777777778 + a2 = 0 + -0.2777777778 Reorder the terms: 0.2777777778 + -0.2777777778 + 0.9444444444a + a2 = 0 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + 0.9444444444a + a2 = 0 + -0.2777777778 0.9444444444a + a2 = 0 + -0.2777777778 Combine like terms: 0 + -0.2777777778 = -0.2777777778 0.9444444444a + a2 = -0.2777777778 The a term is 0.9444444444a. Take half its coefficient (0.4722222222). Square it (0.2229938271) and add it to both sides. Add '0.2229938271' to each side of the equation. 0.9444444444a + 0.2229938271 + a2 = -0.2777777778 + 0.2229938271 Reorder the terms: 0.2229938271 + 0.9444444444a + a2 = -0.2777777778 + 0.2229938271 Combine like terms: -0.2777777778 + 0.2229938271 = -0.0547839507 0.2229938271 + 0.9444444444a + a2 = -0.0547839507 Factor a perfect square on the left side: (a + 0.4722222222)(a + 0.4722222222) = -0.0547839507 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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