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Simplifying 56a2 + 21215a + 45 = 0 Reorder the terms: 45 + 21215a + 56a2 = 0 Solving 45 + 21215a + 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 + 378.8392857a + a2 = 0 Move the constant term to the right: Add '-0.8035714286' to each side of the equation. 0.8035714286 + 378.8392857a + -0.8035714286 + a2 = 0 + -0.8035714286 Reorder the terms: 0.8035714286 + -0.8035714286 + 378.8392857a + a2 = 0 + -0.8035714286 Combine like terms: 0.8035714286 + -0.8035714286 = 0.0000000000 0.0000000000 + 378.8392857a + a2 = 0 + -0.8035714286 378.8392857a + a2 = 0 + -0.8035714286 Combine like terms: 0 + -0.8035714286 = -0.8035714286 378.8392857a + a2 = -0.8035714286 The a term is 378.8392857a. Take half its coefficient (189.4196429). Square it (35879.80112) and add it to both sides. Add '35879.80112' to each side of the equation. 378.8392857a + 35879.80112 + a2 = -0.8035714286 + 35879.80112 Reorder the terms: 35879.80112 + 378.8392857a + a2 = -0.8035714286 + 35879.80112 Combine like terms: -0.8035714286 + 35879.80112 = 35878.9975485714 35879.80112 + 378.8392857a + a2 = 35878.9975485714 Factor a perfect square on the left side: (a + 189.4196429)(a + 189.4196429) = 35878.9975485714 Calculate the square root of the right side: 189.417521757 Break this problem into two subproblems by setting (a + 189.4196429) equal to 189.417521757 and -189.417521757.Subproblem 1
a + 189.4196429 = 189.417521757 Simplifying a + 189.4196429 = 189.417521757 Reorder the terms: 189.4196429 + a = 189.417521757 Solving 189.4196429 + a = 189.417521757 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-189.4196429' to each side of the equation. 189.4196429 + -189.4196429 + a = 189.417521757 + -189.4196429 Combine like terms: 189.4196429 + -189.4196429 = 0.0000000 0.0000000 + a = 189.417521757 + -189.4196429 a = 189.417521757 + -189.4196429 Combine like terms: 189.417521757 + -189.4196429 = -0.002121143 a = -0.002121143 Simplifying a = -0.002121143Subproblem 2
a + 189.4196429 = -189.417521757 Simplifying a + 189.4196429 = -189.417521757 Reorder the terms: 189.4196429 + a = -189.417521757 Solving 189.4196429 + a = -189.417521757 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-189.4196429' to each side of the equation. 189.4196429 + -189.4196429 + a = -189.417521757 + -189.4196429 Combine like terms: 189.4196429 + -189.4196429 = 0.0000000 0.0000000 + a = -189.417521757 + -189.4196429 a = -189.417521757 + -189.4196429 Combine like terms: -189.417521757 + -189.4196429 = -378.837164657 a = -378.837164657 Simplifying a = -378.837164657Solution
The solution to the problem is based on the solutions from the subproblems. a = {-0.002121143, -378.837164657}
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