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Simplifying 11a2 + 11a = 4 Reorder the terms: 11a + 11a2 = 4 Solving 11a + 11a2 = 4 Solving for variable 'a'. Reorder the terms: -4 + 11a + 11a2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 11a + 11a2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.3636363636 + a + a2 = 0 Move the constant term to the right: Add '0.3636363636' to each side of the equation. -0.3636363636 + a + 0.3636363636 + a2 = 0 + 0.3636363636 Reorder the terms: -0.3636363636 + 0.3636363636 + a + a2 = 0 + 0.3636363636 Combine like terms: -0.3636363636 + 0.3636363636 = 0.0000000000 0.0000000000 + a + a2 = 0 + 0.3636363636 a + a2 = 0 + 0.3636363636 Combine like terms: 0 + 0.3636363636 = 0.3636363636 a + a2 = 0.3636363636 The a term is a. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + a2 = 0.3636363636 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + a2 = 0.3636363636 + 0.25 Combine like terms: 0.3636363636 + 0.25 = 0.6136363636 1.25 + a2 = 0.6136363636 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 0.6136363636 Calculate the square root of the right side: 0.783349452 Break this problem into two subproblems by setting (a + 0.5) equal to 0.783349452 and -0.783349452.Subproblem 1
a + 0.5 = 0.783349452 Simplifying a + 0.5 = 0.783349452 Reorder the terms: 0.5 + a = 0.783349452 Solving 0.5 + a = 0.783349452 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = 0.783349452 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 0.783349452 + -0.5 a = 0.783349452 + -0.5 Combine like terms: 0.783349452 + -0.5 = 0.283349452 a = 0.283349452 Simplifying a = 0.283349452Subproblem 2
a + 0.5 = -0.783349452 Simplifying a + 0.5 = -0.783349452 Reorder the terms: 0.5 + a = -0.783349452 Solving 0.5 + a = -0.783349452 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + a = -0.783349452 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -0.783349452 + -0.5 a = -0.783349452 + -0.5 Combine like terms: -0.783349452 + -0.5 = -1.283349452 a = -1.283349452 Simplifying a = -1.283349452Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.283349452, -1.283349452}
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