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Simplifying (11a2 + -15a + -4) + -1(-9a2 + a + 6) = 0 Reorder the terms: (-4 + -15a + 11a2) + -1(-9a2 + a + 6) = 0 Remove parenthesis around (-4 + -15a + 11a2) -4 + -15a + 11a2 + -1(-9a2 + a + 6) = 0 Reorder the terms: -4 + -15a + 11a2 + -1(6 + a + -9a2) = 0 -4 + -15a + 11a2 + (6 * -1 + a * -1 + -9a2 * -1) = 0 -4 + -15a + 11a2 + (-6 + -1a + 9a2) = 0 Reorder the terms: -4 + -6 + -15a + -1a + 11a2 + 9a2 = 0 Combine like terms: -4 + -6 = -10 -10 + -15a + -1a + 11a2 + 9a2 = 0 Combine like terms: -15a + -1a = -16a -10 + -16a + 11a2 + 9a2 = 0 Combine like terms: 11a2 + 9a2 = 20a2 -10 + -16a + 20a2 = 0 Solving -10 + -16a + 20a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -8a + 10a2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -8a + 10a2)' equal to zero and attempt to solve: Simplifying -5 + -8a + 10a2 = 0 Solving -5 + -8a + 10a2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.5 + -0.8a + a2 = 0.0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.8a + 0.5 + a2 = 0.0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.8a + a2 = 0.0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.8a + a2 = 0.0 + 0.5 -0.8a + a2 = 0.0 + 0.5 Combine like terms: 0.0 + 0.5 = 0.5 -0.8a + a2 = 0.5 The a term is -0.8a. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8a + 0.16 + a2 = 0.5 + 0.16 Reorder the terms: 0.16 + -0.8a + a2 = 0.5 + 0.16 Combine like terms: 0.5 + 0.16 = 0.66 0.16 + -0.8a + a2 = 0.66 Factor a perfect square on the left side: (a + -0.4)(a + -0.4) = 0.66 Calculate the square root of the right side: 0.81240384 Break this problem into two subproblems by setting (a + -0.4) equal to 0.81240384 and -0.81240384.Subproblem 1
a + -0.4 = 0.81240384 Simplifying a + -0.4 = 0.81240384 Reorder the terms: -0.4 + a = 0.81240384 Solving -0.4 + a = 0.81240384 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + a = 0.81240384 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + a = 0.81240384 + 0.4 a = 0.81240384 + 0.4 Combine like terms: 0.81240384 + 0.4 = 1.21240384 a = 1.21240384 Simplifying a = 1.21240384Subproblem 2
a + -0.4 = -0.81240384 Simplifying a + -0.4 = -0.81240384 Reorder the terms: -0.4 + a = -0.81240384 Solving -0.4 + a = -0.81240384 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + a = -0.81240384 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + a = -0.81240384 + 0.4 a = -0.81240384 + 0.4 Combine like terms: -0.81240384 + 0.4 = -0.41240384 a = -0.41240384 Simplifying a = -0.41240384Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.21240384, -0.41240384}Solution
a = {1.21240384, -0.41240384}
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