(x+2.5)(x+2.5)=3.25

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Solution for (x+2.5)(x+2.5)=3.25 equation: 


Simplifying
(x + 2.5)(x + 2.5) = 3.25

Reorder the terms:
(2.5 + x)(x + 2.5) = 3.25

Reorder the terms:
(2.5 + x)(2.5 + x) = 3.25

Multiply (2.5 + x) * (2.5 + x)
(2.5(2.5 + x) + x(2.5 + x)) = 3.25
((2.5 * 2.5 + x * 2.5) + x(2.5 + x)) = 3.25
((6.25 + 2.5x) + x(2.5 + x)) = 3.25
(6.25 + 2.5x + (2.5 * x + x * x)) = 3.25
(6.25 + 2.5x + (2.5x + x2)) = 3.25

Combine like terms: 2.5x + 2.5x = 5x
(6.25 + 5x + x2) = 3.25

Solving
6.25 + 5x + x2 = 3.25

Solving for variable 'x'.

Reorder the terms:
6.25 + -3.25 + 5x + x2 = 3.25 + -3.25

Combine like terms: 6.25 + -3.25 = 3
3 + 5x + x2 = 3.25 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
3 + 5x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 5x + -3 + x2 = 0.00 + -3

Reorder the terms:
3 + -3 + 5x + x2 = 0.00 + -3

Combine like terms: 3 + -3 = 0
0 + 5x + x2 = 0.00 + -3
5x + x2 = 0.00 + -3

Combine like terms: 0.00 + -3 = -3
5x + x2 = -3

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -3 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -3 + 6.25

Combine like terms: -3 + 6.25 = 3.25
6.25 + 5x + x2 = 3.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + 2.5) equal to 1.802775638 and -1.802775638.


Subproblem 1
x + 2.5 = 1.802775638

Simplifying
x + 2.5 = 1.802775638

Reorder the terms:
2.5 + x = 1.802775638

Solving
2.5 + x = 1.802775638

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 1.802775638 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 1.802775638 + -2.5
x = 1.802775638 + -2.5

Combine like terms: 1.802775638 + -2.5 = -0.697224362
x = -0.697224362

Simplifying
x = -0.697224362


Subproblem 2
x + 2.5 = -1.802775638

Simplifying
x + 2.5 = -1.802775638

Reorder the terms:
2.5 + x = -1.802775638

Solving
2.5 + x = -1.802775638

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -1.802775638 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -1.802775638 + -2.5
x = -1.802775638 + -2.5

Combine like terms: -1.802775638 + -2.5 = -4.302775638
x = -4.302775638

Simplifying
x = -4.302775638


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.697224362, -4.302775638}

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