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Simplifying a2 + a + -255 = 0 Reorder the terms: -255 + a + a2 = 0 Solving -255 + a + a2 = 0 Solving for variable 'a'. Begin completing the square. Move the constant term to the right: Add '255' to each side of the equation. -255 + a + 255 + a2 = 0 + 255 Reorder the terms: -255 + 255 + a + a2 = 0 + 255 Combine like terms: -255 + 255 = 0 0 + a + a2 = 0 + 255 a + a2 = 0 + 255 Combine like terms: 0 + 255 = 255 a + a2 = 255 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 = 255 + 0.25 Reorder the terms: 0.25 + a + a2 = 255 + 0.25 Combine like terms: 255 + 0.25 = 255.25 0.25 + a + a2 = 255.25 Factor a perfect square on the left side: (a + 0.5)(a + 0.5) = 255.25 Calculate the square root of the right side: 15.976545309 Break this problem into two subproblems by setting (a + 0.5) equal to 15.976545309 and -15.976545309.Subproblem 1
a + 0.5 = 15.976545309 Simplifying a + 0.5 = 15.976545309 Reorder the terms: 0.5 + a = 15.976545309 Solving 0.5 + a = 15.976545309 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 = 15.976545309 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = 15.976545309 + -0.5 a = 15.976545309 + -0.5 Combine like terms: 15.976545309 + -0.5 = 15.476545309 a = 15.476545309 Simplifying a = 15.476545309Subproblem 2
a + 0.5 = -15.976545309 Simplifying a + 0.5 = -15.976545309 Reorder the terms: 0.5 + a = -15.976545309 Solving 0.5 + a = -15.976545309 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 = -15.976545309 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + a = -15.976545309 + -0.5 a = -15.976545309 + -0.5 Combine like terms: -15.976545309 + -0.5 = -16.476545309 a = -16.476545309 Simplifying a = -16.476545309Solution
The solution to the problem is based on the solutions from the subproblems. a = {15.476545309, -16.476545309}
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