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Simplifying (a2 + -3a + -5) + -1(-1a2 + -7a + 4) = 0 Reorder the terms: (-5 + -3a + a2) + -1(-1a2 + -7a + 4) = 0 Remove parenthesis around (-5 + -3a + a2) -5 + -3a + a2 + -1(-1a2 + -7a + 4) = 0 Reorder the terms: -5 + -3a + a2 + -1(4 + -7a + -1a2) = 0 -5 + -3a + a2 + (4 * -1 + -7a * -1 + -1a2 * -1) = 0 -5 + -3a + a2 + (-4 + 7a + 1a2) = 0 Reorder the terms: -5 + -4 + -3a + 7a + a2 + 1a2 = 0 Combine like terms: -5 + -4 = -9 -9 + -3a + 7a + a2 + 1a2 = 0 Combine like terms: -3a + 7a = 4a -9 + 4a + a2 + 1a2 = 0 Combine like terms: a2 + 1a2 = 2a2 -9 + 4a + 2a2 = 0 Solving -9 + 4a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + 2a + a2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + 2a + 4.5 + a2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + 2a + a2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + 2a + a2 = 0 + 4.5 2a + a2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 2a + a2 = 4.5 The a term is 2a. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2a + 1 + a2 = 4.5 + 1 Reorder the terms: 1 + 2a + a2 = 4.5 + 1 Combine like terms: 4.5 + 1 = 5.5 1 + 2a + a2 = 5.5 Factor a perfect square on the left side: (a + 1)(a + 1) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (a + 1) equal to 2.34520788 and -2.34520788.Subproblem 1
a + 1 = 2.34520788 Simplifying a + 1 = 2.34520788 Reorder the terms: 1 + a = 2.34520788 Solving 1 + a = 2.34520788 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 2.34520788 + -1 Combine like terms: 1 + -1 = 0 0 + a = 2.34520788 + -1 a = 2.34520788 + -1 Combine like terms: 2.34520788 + -1 = 1.34520788 a = 1.34520788 Simplifying a = 1.34520788Subproblem 2
a + 1 = -2.34520788 Simplifying a + 1 = -2.34520788 Reorder the terms: 1 + a = -2.34520788 Solving 1 + a = -2.34520788 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = -2.34520788 + -1 Combine like terms: 1 + -1 = 0 0 + a = -2.34520788 + -1 a = -2.34520788 + -1 Combine like terms: -2.34520788 + -1 = -3.34520788 a = -3.34520788 Simplifying a = -3.34520788Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.34520788, -3.34520788}
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