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Simplifying a2 + -1a + -13 = 0 Reorder the terms: -13 + -1a + a2 = 0 Solving -13 + -1a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -1a + 13 + a2 = 0 + 13 Reorder the terms: -13 + 13 + -1a + a2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -1a + a2 = 0 + 13 -1a + a2 = 0 + 13 Combine like terms: 0 + 13 = 13 -1a + a2 = 13 The a term is -1a. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1a + 0.25 + a2 = 13 + 0.25 Reorder the terms: 0.25 + -1a + a2 = 13 + 0.25 Combine like terms: 13 + 0.25 = 13.25 0.25 + -1a + a2 = 13.25 Factor a perfect square on the left side: (a + -0.5)(a + -0.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (a + -0.5) equal to 3.640054945 and -3.640054945.Subproblem 1
a + -0.5 = 3.640054945 Simplifying a + -0.5 = 3.640054945 Reorder the terms: -0.5 + a = 3.640054945 Solving -0.5 + a = 3.640054945 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a = 3.640054945 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = 3.640054945 + 0.5 a = 3.640054945 + 0.5 Combine like terms: 3.640054945 + 0.5 = 4.140054945 a = 4.140054945 Simplifying a = 4.140054945Subproblem 2
a + -0.5 = -3.640054945 Simplifying a + -0.5 = -3.640054945 Reorder the terms: -0.5 + a = -3.640054945 Solving -0.5 + a = -3.640054945 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + a = -3.640054945 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + a = -3.640054945 + 0.5 a = -3.640054945 + 0.5 Combine like terms: -3.640054945 + 0.5 = -3.140054945 a = -3.140054945 Simplifying a = -3.140054945Solution
The solution to the problem is based on the solutions from the subproblems. a = {4.140054945, -3.140054945}
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