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Simplifying a2 + 13a = 12 Reorder the terms: 13a + a2 = 12 Solving 13a + a2 = 12 Solving for variable 'a'. Reorder the terms: -12 + 13a + a2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 13a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 13a + 12 + a2 = 0 + 12 Reorder the terms: -12 + 12 + 13a + a2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 13a + a2 = 0 + 12 13a + a2 = 0 + 12 Combine like terms: 0 + 12 = 12 13a + a2 = 12 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 = 12 + 42.25 Reorder the terms: 42.25 + 13a + a2 = 12 + 42.25 Combine like terms: 12 + 42.25 = 54.25 42.25 + 13a + a2 = 54.25 Factor a perfect square on the left side: (a + 6.5)(a + 6.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (a + 6.5) equal to 7.365459931 and -7.365459931.Subproblem 1
a + 6.5 = 7.365459931 Simplifying a + 6.5 = 7.365459931 Reorder the terms: 6.5 + a = 7.365459931 Solving 6.5 + a = 7.365459931 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 = 7.365459931 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + a = 7.365459931 + -6.5 a = 7.365459931 + -6.5 Combine like terms: 7.365459931 + -6.5 = 0.865459931 a = 0.865459931 Simplifying a = 0.865459931Subproblem 2
a + 6.5 = -7.365459931 Simplifying a + 6.5 = -7.365459931 Reorder the terms: 6.5 + a = -7.365459931 Solving 6.5 + a = -7.365459931 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 = -7.365459931 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + a = -7.365459931 + -6.5 a = -7.365459931 + -6.5 Combine like terms: -7.365459931 + -6.5 = -13.865459931 a = -13.865459931 Simplifying a = -13.865459931Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.865459931, -13.865459931}
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