x(x+1.3)=63.5

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Solution for x(x+1.3)=63.5 equation: 


Simplifying
x(x + 1.3) = 63.5

Reorder the terms:
x(1.3 + x) = 63.5
(1.3 * x + x * x) = 63.5
(1.3x + x2) = 63.5

Solving
1.3x + x2 = 63.5

Solving for variable 'x'.

Reorder the terms:
-63.5 + 1.3x + x2 = 63.5 + -63.5

Combine like terms: 63.5 + -63.5 = 0.0
-63.5 + 1.3x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '63.5' to each side of the equation.
-63.5 + 1.3x + 63.5 + x2 = 0.0 + 63.5

Reorder the terms:
-63.5 + 63.5 + 1.3x + x2 = 0.0 + 63.5

Combine like terms: -63.5 + 63.5 = 0.0
0.0 + 1.3x + x2 = 0.0 + 63.5
1.3x + x2 = 0.0 + 63.5

Combine like terms: 0.0 + 63.5 = 63.5
1.3x + x2 = 63.5

The x term is 1.3x.  Take half its coefficient (0.65).
Square it (0.4225) and add it to both sides.

Add '0.4225' to each side of the equation.
1.3x + 0.4225 + x2 = 63.5 + 0.4225

Reorder the terms:
0.4225 + 1.3x + x2 = 63.5 + 0.4225

Combine like terms: 63.5 + 0.4225 = 63.9225
0.4225 + 1.3x + x2 = 63.9225

Factor a perfect square on the left side:
(x + 0.65)(x + 0.65) = 63.9225

Calculate the square root of the right side: 7.995154783

Break this problem into two subproblems by setting 
(x + 0.65) equal to 7.995154783 and -7.995154783.


Subproblem 1
x + 0.65 = 7.995154783

Simplifying
x + 0.65 = 7.995154783

Reorder the terms:
0.65 + x = 7.995154783

Solving
0.65 + x = 7.995154783

Solving for variable 'x'.

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

Add '-0.65' to each side of the equation.
0.65 + -0.65 + x = 7.995154783 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + x = 7.995154783 + -0.65
x = 7.995154783 + -0.65

Combine like terms: 7.995154783 + -0.65 = 7.345154783
x = 7.345154783

Simplifying
x = 7.345154783


Subproblem 2
x + 0.65 = -7.995154783

Simplifying
x + 0.65 = -7.995154783

Reorder the terms:
0.65 + x = -7.995154783

Solving
0.65 + x = -7.995154783

Solving for variable 'x'.

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

Add '-0.65' to each side of the equation.
0.65 + -0.65 + x = -7.995154783 + -0.65

Combine like terms: 0.65 + -0.65 = 0.00
0.00 + x = -7.995154783 + -0.65
x = -7.995154783 + -0.65

Combine like terms: -7.995154783 + -0.65 = -8.645154783
x = -8.645154783

Simplifying
x = -8.645154783


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.345154783, -8.645154783}

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