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Simplifying 11a2 = -10a + 16 Reorder the terms: 11a2 = 16 + -10a Solving 11a2 = 16 + -10a Solving for variable 'a'. Reorder the terms: -16 + 10a + 11a2 = 16 + -10a + -16 + 10a Reorder the terms: -16 + 10a + 11a2 = 16 + -16 + -10a + 10a Combine like terms: 16 + -16 = 0 -16 + 10a + 11a2 = 0 + -10a + 10a -16 + 10a + 11a2 = -10a + 10a Combine like terms: -10a + 10a = 0 -16 + 10a + 11a2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.454545455 + 0.9090909091a + a2 = 0 Move the constant term to the right: Add '1.454545455' to each side of the equation. -1.454545455 + 0.9090909091a + 1.454545455 + a2 = 0 + 1.454545455 Reorder the terms: -1.454545455 + 1.454545455 + 0.9090909091a + a2 = 0 + 1.454545455 Combine like terms: -1.454545455 + 1.454545455 = 0.000000000 0.000000000 + 0.9090909091a + a2 = 0 + 1.454545455 0.9090909091a + a2 = 0 + 1.454545455 Combine like terms: 0 + 1.454545455 = 1.454545455 0.9090909091a + a2 = 1.454545455 The a term is 0.9090909091a. Take half its coefficient (0.4545454546). Square it (0.2066115703) and add it to both sides. Add '0.2066115703' to each side of the equation. 0.9090909091a + 0.2066115703 + a2 = 1.454545455 + 0.2066115703 Reorder the terms: 0.2066115703 + 0.9090909091a + a2 = 1.454545455 + 0.2066115703 Combine like terms: 1.454545455 + 0.2066115703 = 1.6611570253 0.2066115703 + 0.9090909091a + a2 = 1.6611570253 Factor a perfect square on the left side: (a + 0.4545454546)(a + 0.4545454546) = 1.6611570253 Calculate the square root of the right side: 1.288858807 Break this problem into two subproblems by setting (a + 0.4545454546) equal to 1.288858807 and -1.288858807.Subproblem 1
a + 0.4545454546 = 1.288858807 Simplifying a + 0.4545454546 = 1.288858807 Reorder the terms: 0.4545454546 + a = 1.288858807 Solving 0.4545454546 + a = 1.288858807 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.4545454546' to each side of the equation. 0.4545454546 + -0.4545454546 + a = 1.288858807 + -0.4545454546 Combine like terms: 0.4545454546 + -0.4545454546 = 0.0000000000 0.0000000000 + a = 1.288858807 + -0.4545454546 a = 1.288858807 + -0.4545454546 Combine like terms: 1.288858807 + -0.4545454546 = 0.8343133524 a = 0.8343133524 Simplifying a = 0.8343133524Subproblem 2
a + 0.4545454546 = -1.288858807 Simplifying a + 0.4545454546 = -1.288858807 Reorder the terms: 0.4545454546 + a = -1.288858807 Solving 0.4545454546 + a = -1.288858807 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.4545454546' to each side of the equation. 0.4545454546 + -0.4545454546 + a = -1.288858807 + -0.4545454546 Combine like terms: 0.4545454546 + -0.4545454546 = 0.0000000000 0.0000000000 + a = -1.288858807 + -0.4545454546 a = -1.288858807 + -0.4545454546 Combine like terms: -1.288858807 + -0.4545454546 = -1.7434042616 a = -1.7434042616 Simplifying a = -1.7434042616Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.8343133524, -1.7434042616}
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