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Simplifying -29a2 + -62a + 2 = 0 Reorder the terms: 2 + -62a + -29a2 = 0 Solving 2 + -62a + -29a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by -29 the coefficient of the squared term: Divide each side by '-29'. -0.06896551724 + 2.137931034a + a2 = 0 Move the constant term to the right: Add '0.06896551724' to each side of the equation. -0.06896551724 + 2.137931034a + 0.06896551724 + a2 = 0 + 0.06896551724 Reorder the terms: -0.06896551724 + 0.06896551724 + 2.137931034a + a2 = 0 + 0.06896551724 Combine like terms: -0.06896551724 + 0.06896551724 = 0.00000000000 0.00000000000 + 2.137931034a + a2 = 0 + 0.06896551724 2.137931034a + a2 = 0 + 0.06896551724 Combine like terms: 0 + 0.06896551724 = 0.06896551724 2.137931034a + a2 = 0.06896551724 The a term is 2.137931034a. Take half its coefficient (1.068965517). Square it (1.142687277) and add it to both sides. Add '1.142687277' to each side of the equation. 2.137931034a + 1.142687277 + a2 = 0.06896551724 + 1.142687277 Reorder the terms: 1.142687277 + 2.137931034a + a2 = 0.06896551724 + 1.142687277 Combine like terms: 0.06896551724 + 1.142687277 = 1.21165279424 1.142687277 + 2.137931034a + a2 = 1.21165279424 Factor a perfect square on the left side: (a + 1.068965517)(a + 1.068965517) = 1.21165279424 Calculate the square root of the right side: 1.100751014 Break this problem into two subproblems by setting (a + 1.068965517) equal to 1.100751014 and -1.100751014.Subproblem 1
a + 1.068965517 = 1.100751014 Simplifying a + 1.068965517 = 1.100751014 Reorder the terms: 1.068965517 + a = 1.100751014 Solving 1.068965517 + a = 1.100751014 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.068965517' to each side of the equation. 1.068965517 + -1.068965517 + a = 1.100751014 + -1.068965517 Combine like terms: 1.068965517 + -1.068965517 = 0.000000000 0.000000000 + a = 1.100751014 + -1.068965517 a = 1.100751014 + -1.068965517 Combine like terms: 1.100751014 + -1.068965517 = 0.031785497 a = 0.031785497 Simplifying a = 0.031785497Subproblem 2
a + 1.068965517 = -1.100751014 Simplifying a + 1.068965517 = -1.100751014 Reorder the terms: 1.068965517 + a = -1.100751014 Solving 1.068965517 + a = -1.100751014 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.068965517' to each side of the equation. 1.068965517 + -1.068965517 + a = -1.100751014 + -1.068965517 Combine like terms: 1.068965517 + -1.068965517 = 0.000000000 0.000000000 + a = -1.100751014 + -1.068965517 a = -1.100751014 + -1.068965517 Combine like terms: -1.100751014 + -1.068965517 = -2.169716531 a = -2.169716531 Simplifying a = -2.169716531Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.031785497, -2.169716531}
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