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Simplifying 2a2 + -13a + 1 = 0 Reorder the terms: 1 + -13a + 2a2 = 0 Solving 1 + -13a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -6.5a + a2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -6.5a + -0.5 + a2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -6.5a + a2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -6.5a + a2 = 0 + -0.5 -6.5a + a2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -6.5a + a2 = -0.5 The a term is -6.5a. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5a + 10.5625 + a2 = -0.5 + 10.5625 Reorder the terms: 10.5625 + -6.5a + a2 = -0.5 + 10.5625 Combine like terms: -0.5 + 10.5625 = 10.0625 10.5625 + -6.5a + a2 = 10.0625 Factor a perfect square on the left side: (a + -3.25)(a + -3.25) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (a + -3.25) equal to 3.172144385 and -3.172144385.Subproblem 1
a + -3.25 = 3.172144385 Simplifying a + -3.25 = 3.172144385 Reorder the terms: -3.25 + a = 3.172144385 Solving -3.25 + a = 3.172144385 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + a = 3.172144385 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + a = 3.172144385 + 3.25 a = 3.172144385 + 3.25 Combine like terms: 3.172144385 + 3.25 = 6.422144385 a = 6.422144385 Simplifying a = 6.422144385Subproblem 2
a + -3.25 = -3.172144385 Simplifying a + -3.25 = -3.172144385 Reorder the terms: -3.25 + a = -3.172144385 Solving -3.25 + a = -3.172144385 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + a = -3.172144385 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + a = -3.172144385 + 3.25 a = -3.172144385 + 3.25 Combine like terms: -3.172144385 + 3.25 = 0.077855615 a = 0.077855615 Simplifying a = 0.077855615Solution
The solution to the problem is based on the solutions from the subproblems. a = {6.422144385, 0.077855615}
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