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Simplifying (0.8a + -0.3)(0.13a + 1) = 0 Reorder the terms: (-0.3 + 0.8a)(0.13a + 1) = 0 Reorder the terms: (-0.3 + 0.8a)(1 + 0.13a) = 0 Multiply (-0.3 + 0.8a) * (1 + 0.13a) (-0.3(1 + 0.13a) + 0.8a * (1 + 0.13a)) = 0 ((1 * -0.3 + 0.13a * -0.3) + 0.8a * (1 + 0.13a)) = 0 ((-0.3 + -0.039a) + 0.8a * (1 + 0.13a)) = 0 (-0.3 + -0.039a + (1 * 0.8a + 0.13a * 0.8a)) = 0 (-0.3 + -0.039a + (0.8a + 0.104a2)) = 0 Combine like terms: -0.039a + 0.8a = 0.761a (-0.3 + 0.761a + 0.104a2) = 0 Solving -0.3 + 0.761a + 0.104a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 0.104 the coefficient of the squared term: Divide each side by '0.104'. -2.884615385 + 7.317307692a + a2 = 0 Move the constant term to the right: Add '2.884615385' to each side of the equation. -2.884615385 + 7.317307692a + 2.884615385 + a2 = 0 + 2.884615385 Reorder the terms: -2.884615385 + 2.884615385 + 7.317307692a + a2 = 0 + 2.884615385 Combine like terms: -2.884615385 + 2.884615385 = 0.000000000 0.000000000 + 7.317307692a + a2 = 0 + 2.884615385 7.317307692a + a2 = 0 + 2.884615385 Combine like terms: 0 + 2.884615385 = 2.884615385 7.317307692a + a2 = 2.884615385 The a term is 7.317307692a. Take half its coefficient (3.658653846). Square it (13.38574796) and add it to both sides. Add '13.38574796' to each side of the equation. 7.317307692a + 13.38574796 + a2 = 2.884615385 + 13.38574796 Reorder the terms: 13.38574796 + 7.317307692a + a2 = 2.884615385 + 13.38574796 Combine like terms: 2.884615385 + 13.38574796 = 16.270363345 13.38574796 + 7.317307692a + a2 = 16.270363345 Factor a perfect square on the left side: (a + 3.658653846)(a + 3.658653846) = 16.270363345 Calculate the square root of the right side: 4.033653845 Break this problem into two subproblems by setting (a + 3.658653846) equal to 4.033653845 and -4.033653845.Subproblem 1
a + 3.658653846 = 4.033653845 Simplifying a + 3.658653846 = 4.033653845 Reorder the terms: 3.658653846 + a = 4.033653845 Solving 3.658653846 + a = 4.033653845 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.658653846' to each side of the equation. 3.658653846 + -3.658653846 + a = 4.033653845 + -3.658653846 Combine like terms: 3.658653846 + -3.658653846 = 0.000000000 0.000000000 + a = 4.033653845 + -3.658653846 a = 4.033653845 + -3.658653846 Combine like terms: 4.033653845 + -3.658653846 = 0.374999999 a = 0.374999999 Simplifying a = 0.374999999Subproblem 2
a + 3.658653846 = -4.033653845 Simplifying a + 3.658653846 = -4.033653845 Reorder the terms: 3.658653846 + a = -4.033653845 Solving 3.658653846 + a = -4.033653845 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.658653846' to each side of the equation. 3.658653846 + -3.658653846 + a = -4.033653845 + -3.658653846 Combine like terms: 3.658653846 + -3.658653846 = 0.000000000 0.000000000 + a = -4.033653845 + -3.658653846 a = -4.033653845 + -3.658653846 Combine like terms: -4.033653845 + -3.658653846 = -7.692307691 a = -7.692307691 Simplifying a = -7.692307691Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.374999999, -7.692307691}
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