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Simplifying a2 + a + -121 = 0 Reorder the terms: -121 + a + a2 = 0 Solving -121 + a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '121' to each side of the equation. -121 + a + 121 + a2 = 0 + 121 Reorder the terms: -121 + 121 + a + a2 = 0 + 121 Combine like terms: -121 + 121 = 0 0 + a + a2 = 0 + 121 a + a2 = 0 + 121 Combine like terms: 0 + 121 = 121 a + a2 = 121 The a term is a. 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. a + 0.25 + a2 = 121 + 0.25 Reorder the terms: 0.25 + a + a2 = 121 + 0.25 Combine like terms: 121 + 0.25 = 121.25 0.25 + a + a2 = 121.25 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 121.25 Calculate the square root of the right side: 11.011357773 Break this problem into two subproblems by setting (a + 0.5) equal to 11.011357773 and -11.011357773.Subproblem 1
a + 0.5 = 11.011357773 Simplifying a + 0.5 = 11.011357773 Reorder the terms: 0.5 + a = 11.011357773 Solving 0.5 + a = 11.011357773 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 = 11.011357773 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 11.011357773 + -0.5 a = 11.011357773 + -0.5 Combine like terms: 11.011357773 + -0.5 = 10.511357773 a = 10.511357773 Simplifying a = 10.511357773Subproblem 2
a + 0.5 = -11.011357773 Simplifying a + 0.5 = -11.011357773 Reorder the terms: 0.5 + a = -11.011357773 Solving 0.5 + a = -11.011357773 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 = -11.011357773 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -11.011357773 + -0.5 a = -11.011357773 + -0.5 Combine like terms: -11.011357773 + -0.5 = -11.511357773 a = -11.511357773 Simplifying a = -11.511357773Solution
The solution to the problem is based on the solutions from the subproblems. a = {10.511357773, -11.511357773}
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