a^2+a-255=0

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Solution for a^2+a-255=0 equation:


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 = 15.476545309

Subproblem 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 = -16.476545309

Solution

The solution to the problem is based on the solutions from the subproblems. a = {15.476545309, -16.476545309}

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