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Simplifying -3(a + -2) + -1a2 = 8a Reorder the terms: -3(-2 + a) + -1a2 = 8a (-2 * -3 + a * -3) + -1a2 = 8a (6 + -3a) + -1a2 = 8a Solving 6 + -3a + -1a2 = 8a Solving for variable 'a'. Reorder the terms: 6 + -3a + -8a + -1a2 = 8a + -8a Combine like terms: -3a + -8a = -11a 6 + -11a + -1a2 = 8a + -8a Combine like terms: 8a + -8a = 0 6 + -11a + -1a2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6 + 11a + a2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 11a + 6 + a2 = 0 + 6 Reorder the terms: -6 + 6 + 11a + a2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 11a + a2 = 0 + 6 11a + a2 = 0 + 6 Combine like terms: 0 + 6 = 6 11a + a2 = 6 The a term is 11a. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11a + 30.25 + a2 = 6 + 30.25 Reorder the terms: 30.25 + 11a + a2 = 6 + 30.25 Combine like terms: 6 + 30.25 = 36.25 30.25 + 11a + a2 = 36.25 Factor a perfect square on the left side: (a + 5.5)(a + 5.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (a + 5.5) equal to 6.020797289 and -6.020797289.Subproblem 1
a + 5.5 = 6.020797289 Simplifying a + 5.5 = 6.020797289 Reorder the terms: 5.5 + a = 6.020797289 Solving 5.5 + a = 6.020797289 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + a = 6.020797289 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + a = 6.020797289 + -5.5 a = 6.020797289 + -5.5 Combine like terms: 6.020797289 + -5.5 = 0.520797289 a = 0.520797289 Simplifying a = 0.520797289Subproblem 2
a + 5.5 = -6.020797289 Simplifying a + 5.5 = -6.020797289 Reorder the terms: 5.5 + a = -6.020797289 Solving 5.5 + a = -6.020797289 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + a = -6.020797289 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + a = -6.020797289 + -5.5 a = -6.020797289 + -5.5 Combine like terms: -6.020797289 + -5.5 = -11.520797289 a = -11.520797289 Simplifying a = -11.520797289Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.520797289, -11.520797289}
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