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Simplifying 56a2 + 1215a + 45 = 0 Reorder the terms: 45 + 1215a + 56a2 = 0 Solving 45 + 1215a + 56a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 56 the coefficient of the squared term: Divide each side by '56'. 0.8035714286 + 21.69642857a + a2 = 0 Move the constant term to the right: Add '-0.8035714286' to each side of the equation. 0.8035714286 + 21.69642857a + -0.8035714286 + a2 = 0 + -0.8035714286 Reorder the terms: 0.8035714286 + -0.8035714286 + 21.69642857a + a2 = 0 + -0.8035714286 Combine like terms: 0.8035714286 + -0.8035714286 = 0.0000000000 0.0000000000 + 21.69642857a + a2 = 0 + -0.8035714286 21.69642857a + a2 = 0 + -0.8035714286 Combine like terms: 0 + -0.8035714286 = -0.8035714286 21.69642857a + a2 = -0.8035714286 The a term is 21.69642857a. Take half its coefficient (10.84821429). Square it (117.6837533) and add it to both sides. Add '117.6837533' to each side of the equation. 21.69642857a + 117.6837533 + a2 = -0.8035714286 + 117.6837533 Reorder the terms: 117.6837533 + 21.69642857a + a2 = -0.8035714286 + 117.6837533 Combine like terms: -0.8035714286 + 117.6837533 = 116.8801818714 117.6837533 + 21.69642857a + a2 = 116.8801818714 Factor a perfect square on the left side: (a + 10.84821429)(a + 10.84821429) = 116.8801818714 Calculate the square root of the right side: 10.811113813 Break this problem into two subproblems by setting (a + 10.84821429) equal to 10.811113813 and -10.811113813.Subproblem 1
a + 10.84821429 = 10.811113813 Simplifying a + 10.84821429 = 10.811113813 Reorder the terms: 10.84821429 + a = 10.811113813 Solving 10.84821429 + a = 10.811113813 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-10.84821429' to each side of the equation. 10.84821429 + -10.84821429 + a = 10.811113813 + -10.84821429 Combine like terms: 10.84821429 + -10.84821429 = 0.00000000 0.00000000 + a = 10.811113813 + -10.84821429 a = 10.811113813 + -10.84821429 Combine like terms: 10.811113813 + -10.84821429 = -0.037100477 a = -0.037100477 Simplifying a = -0.037100477Subproblem 2
a + 10.84821429 = -10.811113813 Simplifying a + 10.84821429 = -10.811113813 Reorder the terms: 10.84821429 + a = -10.811113813 Solving 10.84821429 + a = -10.811113813 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-10.84821429' to each side of the equation. 10.84821429 + -10.84821429 + a = -10.811113813 + -10.84821429 Combine like terms: 10.84821429 + -10.84821429 = 0.00000000 0.00000000 + a = -10.811113813 + -10.84821429 a = -10.811113813 + -10.84821429 Combine like terms: -10.811113813 + -10.84821429 = -21.659328103 a = -21.659328103 Simplifying a = -21.659328103Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.037100477, -21.659328103}
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