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Simplifying a2 + 11a + -22 = 0 Reorder the terms: -22 + 11a + a2 = 0 Solving -22 + 11a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 11a + 22 + a2 = 0 + 22 Reorder the terms: -22 + 22 + 11a + a2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 11a + a2 = 0 + 22 11a + a2 = 0 + 22 Combine like terms: 0 + 22 = 22 11a + a2 = 22 The a term is 11a. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11a + 30.25 + a2 = 22 + 30.25 Reorder the terms: 30.25 + 11a + a2 = 22 + 30.25 Combine like terms: 22 + 30.25 = 52.25 30.25 + 11a + a2 = 52.25 Factor a perfect square on the left side: (a + 5.5)(a + 5.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (a + 5.5) equal to 7.228416147 and -7.228416147.Subproblem 1
a + 5.5 = 7.228416147 Simplifying a + 5.5 = 7.228416147 Reorder the terms: 5.5 + a = 7.228416147 Solving 5.5 + a = 7.228416147 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + a = 7.228416147 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + a = 7.228416147 + -5.5 a = 7.228416147 + -5.5 Combine like terms: 7.228416147 + -5.5 = 1.728416147 a = 1.728416147 Simplifying a = 1.728416147Subproblem 2
a + 5.5 = -7.228416147 Simplifying a + 5.5 = -7.228416147 Reorder the terms: 5.5 + a = -7.228416147 Solving 5.5 + a = -7.228416147 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + a = -7.228416147 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + a = -7.228416147 + -5.5 a = -7.228416147 + -5.5 Combine like terms: -7.228416147 + -5.5 = -12.728416147 a = -12.728416147 Simplifying a = -12.728416147Solution
The solution to the problem is based on the solutions from the subproblems. a = {1.728416147, -12.728416147}
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