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Simplifying 11a2 + 2a + -14 = 0 Reorder the terms: -14 + 2a + 11a2 = 0 Solving -14 + 2a + 11a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.272727273 + 0.1818181818a + a2 = 0 Move the constant term to the right: Add '1.272727273' to each side of the equation. -1.272727273 + 0.1818181818a + 1.272727273 + a2 = 0 + 1.272727273 Reorder the terms: -1.272727273 + 1.272727273 + 0.1818181818a + a2 = 0 + 1.272727273 Combine like terms: -1.272727273 + 1.272727273 = 0.000000000 0.000000000 + 0.1818181818a + a2 = 0 + 1.272727273 0.1818181818a + a2 = 0 + 1.272727273 Combine like terms: 0 + 1.272727273 = 1.272727273 0.1818181818a + a2 = 1.272727273 The a term is 0.1818181818a. Take half its coefficient (0.0909090909). Square it (0.008264462808) and add it to both sides. Add '0.008264462808' to each side of the equation. 0.1818181818a + 0.008264462808 + a2 = 1.272727273 + 0.008264462808 Reorder the terms: 0.008264462808 + 0.1818181818a + a2 = 1.272727273 + 0.008264462808 Combine like terms: 1.272727273 + 0.008264462808 = 1.280991735808 0.008264462808 + 0.1818181818a + a2 = 1.280991735808 Factor a perfect square on the left side: (a + 0.0909090909)(a + 0.0909090909) = 1.280991735808 Calculate the square root of the right side: 1.131809054 Break this problem into two subproblems by setting (a + 0.0909090909) equal to 1.131809054 and -1.131809054.Subproblem 1
a + 0.0909090909 = 1.131809054 Simplifying a + 0.0909090909 = 1.131809054 Reorder the terms: 0.0909090909 + a = 1.131809054 Solving 0.0909090909 + a = 1.131809054 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + a = 1.131809054 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + a = 1.131809054 + -0.0909090909 a = 1.131809054 + -0.0909090909 Combine like terms: 1.131809054 + -0.0909090909 = 1.0408999631 a = 1.0408999631 Simplifying a = 1.0408999631Subproblem 2
a + 0.0909090909 = -1.131809054 Simplifying a + 0.0909090909 = -1.131809054 Reorder the terms: 0.0909090909 + a = -1.131809054 Solving 0.0909090909 + a = -1.131809054 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + a = -1.131809054 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + a = -1.131809054 + -0.0909090909 a = -1.131809054 + -0.0909090909 Combine like terms: -1.131809054 + -0.0909090909 = -1.2227181449 a = -1.2227181449 Simplifying a = -1.2227181449Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.0408999631, -1.2227181449}
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