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Simplifying 8a2 + 11a + -8 = 0 Reorder the terms: -8 + 11a + 8a2 = 0 Solving -8 + 11a + 8a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1 + 1.375a + a2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.375a + 1 + a2 = 0 + 1 Reorder the terms: -1 + 1 + 1.375a + a2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.375a + a2 = 0 + 1 1.375a + a2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.375a + a2 = 1 The a term is 1.375a. Take half its coefficient (0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. 1.375a + 0.47265625 + a2 = 1 + 0.47265625 Reorder the terms: 0.47265625 + 1.375a + a2 = 1 + 0.47265625 Combine like terms: 1 + 0.47265625 = 1.47265625 0.47265625 + 1.375a + a2 = 1.47265625 Factor a perfect square on the left side: (a + 0.6875)(a + 0.6875) = 1.47265625 Calculate the square root of the right side: 1.21353049 Break this problem into two subproblems by setting (a + 0.6875) equal to 1.21353049 and -1.21353049.Subproblem 1
a + 0.6875 = 1.21353049 Simplifying a + 0.6875 = 1.21353049 Reorder the terms: 0.6875 + a = 1.21353049 Solving 0.6875 + a = 1.21353049 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + a = 1.21353049 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + a = 1.21353049 + -0.6875 a = 1.21353049 + -0.6875 Combine like terms: 1.21353049 + -0.6875 = 0.52603049 a = 0.52603049 Simplifying a = 0.52603049Subproblem 2
a + 0.6875 = -1.21353049 Simplifying a + 0.6875 = -1.21353049 Reorder the terms: 0.6875 + a = -1.21353049 Solving 0.6875 + a = -1.21353049 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.6875' to each side of the equation. 0.6875 + -0.6875 + a = -1.21353049 + -0.6875 Combine like terms: 0.6875 + -0.6875 = 0.0000 0.0000 + a = -1.21353049 + -0.6875 a = -1.21353049 + -0.6875 Combine like terms: -1.21353049 + -0.6875 = -1.90103049 a = -1.90103049 Simplifying a = -1.90103049Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.52603049, -1.90103049}
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