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Simplifying 11a2 + -32a + 17 = 0 Reorder the terms: 17 + -32a + 11a2 = 0 Solving 17 + -32a + 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'. 1.545454545 + -2.909090909a + a2 = 0 Move the constant term to the right: Add '-1.545454545' to each side of the equation. 1.545454545 + -2.909090909a + -1.545454545 + a2 = 0 + -1.545454545 Reorder the terms: 1.545454545 + -1.545454545 + -2.909090909a + a2 = 0 + -1.545454545 Combine like terms: 1.545454545 + -1.545454545 = 0.000000000 0.000000000 + -2.909090909a + a2 = 0 + -1.545454545 -2.909090909a + a2 = 0 + -1.545454545 Combine like terms: 0 + -1.545454545 = -1.545454545 -2.909090909a + a2 = -1.545454545 The a term is -2.909090909a. Take half its coefficient (-1.454545455). Square it (2.115702481) and add it to both sides. Add '2.115702481' to each side of the equation. -2.909090909a + 2.115702481 + a2 = -1.545454545 + 2.115702481 Reorder the terms: 2.115702481 + -2.909090909a + a2 = -1.545454545 + 2.115702481 Combine like terms: -1.545454545 + 2.115702481 = 0.570247936 2.115702481 + -2.909090909a + a2 = 0.570247936 Factor a perfect square on the left side: (a + -1.454545455)(a + -1.454545455) = 0.570247936 Calculate the square root of the right side: 0.755147625 Break this problem into two subproblems by setting (a + -1.454545455) equal to 0.755147625 and -0.755147625.Subproblem 1
a + -1.454545455 = 0.755147625 Simplifying a + -1.454545455 = 0.755147625 Reorder the terms: -1.454545455 + a = 0.755147625 Solving -1.454545455 + a = 0.755147625 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.454545455' to each side of the equation. -1.454545455 + 1.454545455 + a = 0.755147625 + 1.454545455 Combine like terms: -1.454545455 + 1.454545455 = 0.000000000 0.000000000 + a = 0.755147625 + 1.454545455 a = 0.755147625 + 1.454545455 Combine like terms: 0.755147625 + 1.454545455 = 2.20969308 a = 2.20969308 Simplifying a = 2.20969308Subproblem 2
a + -1.454545455 = -0.755147625 Simplifying a + -1.454545455 = -0.755147625 Reorder the terms: -1.454545455 + a = -0.755147625 Solving -1.454545455 + a = -0.755147625 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.454545455' to each side of the equation. -1.454545455 + 1.454545455 + a = -0.755147625 + 1.454545455 Combine like terms: -1.454545455 + 1.454545455 = 0.000000000 0.000000000 + a = -0.755147625 + 1.454545455 a = -0.755147625 + 1.454545455 Combine like terms: -0.755147625 + 1.454545455 = 0.69939783 a = 0.69939783 Simplifying a = 0.69939783Solution
The solution to the problem is based on the solutions from the subproblems. a = {2.20969308, 0.69939783}
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