1.25a+a^2=2

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Solution for 1.25a+a^2=2 equation: 


Simplifying
1.25a + a2 = 2

Solving
1.25a + a2 = 2

Solving for variable 'a'.

Reorder the terms:
-2 + 1.25a + a2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + 1.25a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 1.25a + 2 + a2 = 0 + 2

Reorder the terms:
-2 + 2 + 1.25a + a2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 1.25a + a2 = 0 + 2
1.25a + a2 = 0 + 2

Combine like terms: 0 + 2 = 2
1.25a + a2 = 2

The a term is 1.25a.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25a + 0.390625 + a2 = 2 + 0.390625

Reorder the terms:
0.390625 + 1.25a + a2 = 2 + 0.390625

Combine like terms: 2 + 0.390625 = 2.390625
0.390625 + 1.25a + a2 = 2.390625

Factor a perfect square on the left side:
(a + 0.625)(a + 0.625) = 2.390625

Calculate the square root of the right side: 1.54616461

Break this problem into two subproblems by setting 
(a + 0.625) equal to 1.54616461 and -1.54616461.


Subproblem 1
a + 0.625 = 1.54616461

Simplifying
a + 0.625 = 1.54616461

Reorder the terms:
0.625 + a = 1.54616461

Solving
0.625 + a = 1.54616461

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-0.625' to each side of the equation.
0.625 + -0.625 + a = 1.54616461 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + a = 1.54616461 + -0.625
a = 1.54616461 + -0.625

Combine like terms: 1.54616461 + -0.625 = 0.92116461
a = 0.92116461

Simplifying
a = 0.92116461


Subproblem 2
a + 0.625 = -1.54616461

Simplifying
a + 0.625 = -1.54616461

Reorder the terms:
0.625 + a = -1.54616461

Solving
0.625 + a = -1.54616461

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-0.625' to each side of the equation.
0.625 + -0.625 + a = -1.54616461 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + a = -1.54616461 + -0.625
a = -1.54616461 + -0.625

Combine like terms: -1.54616461 + -0.625 = -2.17116461
a = -2.17116461

Simplifying
a = -2.17116461


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.92116461, -2.17116461}

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