1.27=x(x+.24)

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Solution for 1.27=x(x+.24) equation: 


Simplifying
1.27 = x(x + 0.24)

Reorder the terms:
1.27 = x(0.24 + x)
1.27 = (0.24 * x + x * x)
1.27 = (0.24x + x2)

Solving
1.27 = 0.24x + x2

Solving for variable 'x'.

Reorder the terms:
1.27 + -0.24x + -1x2 = 0.24x + -0.24x + x2 + -1x2

Combine like terms: 0.24x + -0.24x = 0.00
1.27 + -0.24x + -1x2 = 0.00 + x2 + -1x2
1.27 + -0.24x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1.27 + -0.24x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1.27 + 0.24x + x2 = 0

Move the constant term to the right:

Add '1.27' to each side of the equation.
-1.27 + 0.24x + 1.27 + x2 = 0 + 1.27

Reorder the terms:
-1.27 + 1.27 + 0.24x + x2 = 0 + 1.27

Combine like terms: -1.27 + 1.27 = 0.00
0.00 + 0.24x + x2 = 0 + 1.27
0.24x + x2 = 0 + 1.27

Combine like terms: 0 + 1.27 = 1.27
0.24x + x2 = 1.27

The x term is 0.24x.  Take half its coefficient (0.12).
Square it (0.0144) and add it to both sides.

Add '0.0144' to each side of the equation.
0.24x + 0.0144 + x2 = 1.27 + 0.0144

Reorder the terms:
0.0144 + 0.24x + x2 = 1.27 + 0.0144

Combine like terms: 1.27 + 0.0144 = 1.2844
0.0144 + 0.24x + x2 = 1.2844

Factor a perfect square on the left side:
(x + 0.12)(x + 0.12) = 1.2844

Calculate the square root of the right side: 1.133313725

Break this problem into two subproblems by setting 
(x + 0.12) equal to 1.133313725 and -1.133313725.


Subproblem 1
x + 0.12 = 1.133313725

Simplifying
x + 0.12 = 1.133313725

Reorder the terms:
0.12 + x = 1.133313725

Solving
0.12 + x = 1.133313725

Solving for variable 'x'.

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

Add '-0.12' to each side of the equation.
0.12 + -0.12 + x = 1.133313725 + -0.12

Combine like terms: 0.12 + -0.12 = 0.00
0.00 + x = 1.133313725 + -0.12
x = 1.133313725 + -0.12

Combine like terms: 1.133313725 + -0.12 = 1.013313725
x = 1.013313725

Simplifying
x = 1.013313725


Subproblem 2
x + 0.12 = -1.133313725

Simplifying
x + 0.12 = -1.133313725

Reorder the terms:
0.12 + x = -1.133313725

Solving
0.12 + x = -1.133313725

Solving for variable 'x'.

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

Add '-0.12' to each side of the equation.
0.12 + -0.12 + x = -1.133313725 + -0.12

Combine like terms: 0.12 + -0.12 = 0.00
0.00 + x = -1.133313725 + -0.12
x = -1.133313725 + -0.12

Combine like terms: -1.133313725 + -0.12 = -1.253313725
x = -1.253313725

Simplifying
x = -1.253313725


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.013313725, -1.253313725}

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