(x+6.5)(x)=63.9

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Solution for (x+6.5)(x)=63.9 equation: 


Simplifying
(x + 6.5)(x) = 63.9

Reorder the terms:
(6.5 + x)(x) = 63.9

Reorder the terms for easier multiplication:
x(6.5 + x) = 63.9
(6.5 * x + x * x) = 63.9
(6.5x + x2) = 63.9

Solving
6.5x + x2 = 63.9

Solving for variable 'x'.

Reorder the terms:
-63.9 + 6.5x + x2 = 63.9 + -63.9

Combine like terms: 63.9 + -63.9 = 0.0
-63.9 + 6.5x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '63.9' to each side of the equation.
-63.9 + 6.5x + 63.9 + x2 = 0.0 + 63.9

Reorder the terms:
-63.9 + 63.9 + 6.5x + x2 = 0.0 + 63.9

Combine like terms: -63.9 + 63.9 = 0.0
0.0 + 6.5x + x2 = 0.0 + 63.9
6.5x + x2 = 0.0 + 63.9

Combine like terms: 0.0 + 63.9 = 63.9
6.5x + x2 = 63.9

The x term is 6.5x.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5x + 10.5625 + x2 = 63.9 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = 63.9 + 10.5625

Combine like terms: 63.9 + 10.5625 = 74.4625
10.5625 + 6.5x + x2 = 74.4625

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 74.4625

Calculate the square root of the right side: 8.629165661

Break this problem into two subproblems by setting 
(x + 3.25) equal to 8.629165661 and -8.629165661.


Subproblem 1
x + 3.25 = 8.629165661

Simplifying
x + 3.25 = 8.629165661

Reorder the terms:
3.25 + x = 8.629165661

Solving
3.25 + x = 8.629165661

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = 8.629165661 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = 8.629165661 + -3.25
x = 8.629165661 + -3.25

Combine like terms: 8.629165661 + -3.25 = 5.379165661
x = 5.379165661

Simplifying
x = 5.379165661


Subproblem 2
x + 3.25 = -8.629165661

Simplifying
x + 3.25 = -8.629165661

Reorder the terms:
3.25 + x = -8.629165661

Solving
3.25 + x = -8.629165661

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = -8.629165661 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = -8.629165661 + -3.25
x = -8.629165661 + -3.25

Combine like terms: -8.629165661 + -3.25 = -11.879165661
x = -11.879165661

Simplifying
x = -11.879165661


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.379165661, -11.879165661}

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