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Simplifying 5a2 + 11a + -2 = 0 Reorder the terms: -2 + 11a + 5a2 = 0 Solving -2 + 11a + 5a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + 2.2a + a2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 2.2a + 0.4 + a2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 2.2a + a2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 2.2a + a2 = 0 + 0.4 2.2a + a2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 2.2a + a2 = 0.4 The a term is 2.2a. Take half its coefficient (1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. 2.2a + 1.21 + a2 = 0.4 + 1.21 Reorder the terms: 1.21 + 2.2a + a2 = 0.4 + 1.21 Combine like terms: 0.4 + 1.21 = 1.61 1.21 + 2.2a + a2 = 1.61 Factor a perfect square on the left side: (a + 1.1)(a + 1.1) = 1.61 Calculate the square root of the right side: 1.268857754 Break this problem into two subproblems by setting (a + 1.1) equal to 1.268857754 and -1.268857754.Subproblem 1
a + 1.1 = 1.268857754 Simplifying a + 1.1 = 1.268857754 Reorder the terms: 1.1 + a = 1.268857754 Solving 1.1 + a = 1.268857754 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + a = 1.268857754 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + a = 1.268857754 + -1.1 a = 1.268857754 + -1.1 Combine like terms: 1.268857754 + -1.1 = 0.168857754 a = 0.168857754 Simplifying a = 0.168857754Subproblem 2
a + 1.1 = -1.268857754 Simplifying a + 1.1 = -1.268857754 Reorder the terms: 1.1 + a = -1.268857754 Solving 1.1 + a = -1.268857754 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.1' to each side of the equation. 1.1 + -1.1 + a = -1.268857754 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + a = -1.268857754 + -1.1 a = -1.268857754 + -1.1 Combine like terms: -1.268857754 + -1.1 = -2.368857754 a = -2.368857754 Simplifying a = -2.368857754Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.168857754, -2.368857754}
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