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Simplifying (4a + 2)(3a + -1) + -1(2a + -4)(a + 5) = 0 Reorder the terms: (2 + 4a)(3a + -1) + -1(2a + -4)(a + 5) = 0 Reorder the terms: (2 + 4a)(-1 + 3a) + -1(2a + -4)(a + 5) = 0 Multiply (2 + 4a) * (-1 + 3a) (2(-1 + 3a) + 4a * (-1 + 3a)) + -1(2a + -4)(a + 5) = 0 ((-1 * 2 + 3a * 2) + 4a * (-1 + 3a)) + -1(2a + -4)(a + 5) = 0 ((-2 + 6a) + 4a * (-1 + 3a)) + -1(2a + -4)(a + 5) = 0 (-2 + 6a + (-1 * 4a + 3a * 4a)) + -1(2a + -4)(a + 5) = 0 (-2 + 6a + (-4a + 12a2)) + -1(2a + -4)(a + 5) = 0 Combine like terms: 6a + -4a = 2a (-2 + 2a + 12a2) + -1(2a + -4)(a + 5) = 0 Reorder the terms: -2 + 2a + 12a2 + -1(-4 + 2a)(a + 5) = 0 Reorder the terms: -2 + 2a + 12a2 + -1(-4 + 2a)(5 + a) = 0 Multiply (-4 + 2a) * (5 + a) -2 + 2a + 12a2 + -1(-4(5 + a) + 2a * (5 + a)) = 0 -2 + 2a + 12a2 + -1((5 * -4 + a * -4) + 2a * (5 + a)) = 0 -2 + 2a + 12a2 + -1((-20 + -4a) + 2a * (5 + a)) = 0 -2 + 2a + 12a2 + -1(-20 + -4a + (5 * 2a + a * 2a)) = 0 -2 + 2a + 12a2 + -1(-20 + -4a + (10a + 2a2)) = 0 Combine like terms: -4a + 10a = 6a -2 + 2a + 12a2 + -1(-20 + 6a + 2a2) = 0 -2 + 2a + 12a2 + (-20 * -1 + 6a * -1 + 2a2 * -1) = 0 -2 + 2a + 12a2 + (20 + -6a + -2a2) = 0 Reorder the terms: -2 + 20 + 2a + -6a + 12a2 + -2a2 = 0 Combine like terms: -2 + 20 = 18 18 + 2a + -6a + 12a2 + -2a2 = 0 Combine like terms: 2a + -6a = -4a 18 + -4a + 12a2 + -2a2 = 0 Combine like terms: 12a2 + -2a2 = 10a2 18 + -4a + 10a2 = 0 Solving 18 + -4a + 10a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -2a + 5a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -2a + 5a2)' equal to zero and attempt to solve: Simplifying 9 + -2a + 5a2 = 0 Solving 9 + -2a + 5a2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.8 + -0.4a + a2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + -0.4a + -1.8 + a2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + -0.4a + a2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + -0.4a + a2 = 0 + -1.8 -0.4a + a2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 -0.4a + a2 = -1.8 The a term is -0.4a. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4a + 0.04 + a2 = -1.8 + 0.04 Reorder the terms: 0.04 + -0.4a + a2 = -1.8 + 0.04 Combine like terms: -1.8 + 0.04 = -1.76 0.04 + -0.4a + a2 = -1.76 Factor a perfect square on the left side: (a + -0.2)(a + -0.2) = -1.76 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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