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Simplifying 2a2 + -1a = 186 Reorder the terms: -1a + 2a2 = 186 Solving -1a + 2a2 = 186 Solving for variable 'a'. Reorder the terms: -186 + -1a + 2a2 = 186 + -186 Combine like terms: 186 + -186 = 0 -186 + -1a + 2a2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -93 + -0.5a + a2 = 0 Move the constant term to the right: Add '93' to each side of the equation. -93 + -0.5a + 93 + a2 = 0 + 93 Reorder the terms: -93 + 93 + -0.5a + a2 = 0 + 93 Combine like terms: -93 + 93 = 0 0 + -0.5a + a2 = 0 + 93 -0.5a + a2 = 0 + 93 Combine like terms: 0 + 93 = 93 -0.5a + a2 = 93 The a term is -0.5a. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5a + 0.0625 + a2 = 93 + 0.0625 Reorder the terms: 0.0625 + -0.5a + a2 = 93 + 0.0625 Combine like terms: 93 + 0.0625 = 93.0625 0.0625 + -0.5a + a2 = 93.0625 Factor a perfect square on the left side: (a + -0.25)(a + -0.25) = 93.0625 Calculate the square root of the right side: 9.646890691 Break this problem into two subproblems by setting (a + -0.25) equal to 9.646890691 and -9.646890691.Subproblem 1
a + -0.25 = 9.646890691 Simplifying a + -0.25 = 9.646890691 Reorder the terms: -0.25 + a = 9.646890691 Solving -0.25 + a = 9.646890691 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = 9.646890691 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = 9.646890691 + 0.25 a = 9.646890691 + 0.25 Combine like terms: 9.646890691 + 0.25 = 9.896890691 a = 9.896890691 Simplifying a = 9.896890691Subproblem 2
a + -0.25 = -9.646890691 Simplifying a + -0.25 = -9.646890691 Reorder the terms: -0.25 + a = -9.646890691 Solving -0.25 + a = -9.646890691 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + a = -9.646890691 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + a = -9.646890691 + 0.25 a = -9.646890691 + 0.25 Combine like terms: -9.646890691 + 0.25 = -9.396890691 a = -9.396890691 Simplifying a = -9.396890691Solution
The solution to the problem is based on the solutions from the subproblems. a = {9.896890691, -9.396890691}
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