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Simplifying a2 + 2a + -10 = -11a Reorder the terms: -10 + 2a + a2 = -11a Solving -10 + 2a + a2 = -11a Solving for variable 'a'. Reorder the terms: -10 + 2a + 11a + a2 = -11a + 11a Combine like terms: 2a + 11a = 13a -10 + 13a + a2 = -11a + 11a Combine like terms: -11a + 11a = 0 -10 + 13a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 13a + 10 + a2 = 0 + 10 Reorder the terms: -10 + 10 + 13a + a2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 13a + a2 = 0 + 10 13a + a2 = 0 + 10 Combine like terms: 0 + 10 = 10 13a + a2 = 10 The a term is 13a. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13a + 42.25 + a2 = 10 + 42.25 Reorder the terms: 42.25 + 13a + a2 = 10 + 42.25 Combine like terms: 10 + 42.25 = 52.25 42.25 + 13a + a2 = 52.25 Factor a perfect square on the left side: (a + 6.5)(a + 6.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (a + 6.5) equal to 7.228416147 and -7.228416147.Subproblem 1
a + 6.5 = 7.228416147 Simplifying a + 6.5 = 7.228416147 Reorder the terms: 6.5 + a = 7.228416147 Solving 6.5 + a = 7.228416147 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + a = 7.228416147 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + a = 7.228416147 + -6.5 a = 7.228416147 + -6.5 Combine like terms: 7.228416147 + -6.5 = 0.728416147 a = 0.728416147 Simplifying a = 0.728416147Subproblem 2
a + 6.5 = -7.228416147 Simplifying a + 6.5 = -7.228416147 Reorder the terms: 6.5 + a = -7.228416147 Solving 6.5 + a = -7.228416147 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + a = -7.228416147 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + a = -7.228416147 + -6.5 a = -7.228416147 + -6.5 Combine like terms: -7.228416147 + -6.5 = -13.728416147 a = -13.728416147 Simplifying a = -13.728416147Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.728416147, -13.728416147}
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