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Simplifying (9a2 + 3a + -4) + -1(-6a2 + 6) = 0 Reorder the terms: (-4 + 3a + 9a2) + -1(-6a2 + 6) = 0 Remove parenthesis around (-4 + 3a + 9a2) -4 + 3a + 9a2 + -1(-6a2 + 6) = 0 Reorder the terms: -4 + 3a + 9a2 + -1(6 + -6a2) = 0 -4 + 3a + 9a2 + (6 * -1 + -6a2 * -1) = 0 -4 + 3a + 9a2 + (-6 + 6a2) = 0 Reorder the terms: -4 + -6 + 3a + 9a2 + 6a2 = 0 Combine like terms: -4 + -6 = -10 -10 + 3a + 9a2 + 6a2 = 0 Combine like terms: 9a2 + 6a2 = 15a2 -10 + 3a + 15a2 = 0 Solving -10 + 3a + 15a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.6666666667 + 0.2a + a2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 0.2a + 0.6666666667 + a2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 0.2a + a2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 0.2a + a2 = 0 + 0.6666666667 0.2a + a2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 0.2a + a2 = 0.6666666667 The a term is 0.2a. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2a + 0.01 + a2 = 0.6666666667 + 0.01 Reorder the terms: 0.01 + 0.2a + a2 = 0.6666666667 + 0.01 Combine like terms: 0.6666666667 + 0.01 = 0.6766666667 0.01 + 0.2a + a2 = 0.6766666667 Factor a perfect square on the left side: (a + 0.1)(a + 0.1) = 0.6766666667 Calculate the square root of the right side: 0.822597512 Break this problem into two subproblems by setting (a + 0.1) equal to 0.822597512 and -0.822597512.Subproblem 1
a + 0.1 = 0.822597512 Simplifying a + 0.1 = 0.822597512 Reorder the terms: 0.1 + a = 0.822597512 Solving 0.1 + a = 0.822597512 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + a = 0.822597512 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + a = 0.822597512 + -0.1 a = 0.822597512 + -0.1 Combine like terms: 0.822597512 + -0.1 = 0.722597512 a = 0.722597512 Simplifying a = 0.722597512Subproblem 2
a + 0.1 = -0.822597512 Simplifying a + 0.1 = -0.822597512 Reorder the terms: 0.1 + a = -0.822597512 Solving 0.1 + a = -0.822597512 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + a = -0.822597512 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + a = -0.822597512 + -0.1 a = -0.822597512 + -0.1 Combine like terms: -0.822597512 + -0.1 = -0.922597512 a = -0.922597512 Simplifying a = -0.922597512Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.722597512, -0.922597512}
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