2x(x+5)-3(5-x)=5

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Solution for 2x(x+5)-3(5-x)=5 equation: 


Simplifying
2x(x + 5) + -3(5 + -1x) = 5

Reorder the terms:
2x(5 + x) + -3(5 + -1x) = 5
(5 * 2x + x * 2x) + -3(5 + -1x) = 5
(10x + 2x2) + -3(5 + -1x) = 5
10x + 2x2 + (5 * -3 + -1x * -3) = 5
10x + 2x2 + (-15 + 3x) = 5

Reorder the terms:
-15 + 10x + 3x + 2x2 = 5

Combine like terms: 10x + 3x = 13x
-15 + 13x + 2x2 = 5

Solving
-15 + 13x + 2x2 = 5

Solving for variable 'x'.

Reorder the terms:
-15 + -5 + 13x + 2x2 = 5 + -5

Combine like terms: -15 + -5 = -20
-20 + 13x + 2x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-20 + 13x + 2x2 = 0

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

Divide each side by '2'.
-10 + 6.5x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 6.5x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 6.5x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 6.5x + x2 = 0 + 10
6.5x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
6.5x + x2 = 10

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 = 10 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = 10 + 10.5625

Combine like terms: 10 + 10.5625 = 20.5625
10.5625 + 6.5x + x2 = 20.5625

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 20.5625

Calculate the square root of the right side: 4.534589287

Break this problem into two subproblems by setting 
(x + 3.25) equal to 4.534589287 and -4.534589287.


Subproblem 1
x + 3.25 = 4.534589287

Simplifying
x + 3.25 = 4.534589287

Reorder the terms:
3.25 + x = 4.534589287

Solving
3.25 + x = 4.534589287

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 = 4.534589287 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = 4.534589287 + -3.25
x = 4.534589287 + -3.25

Combine like terms: 4.534589287 + -3.25 = 1.284589287
x = 1.284589287

Simplifying
x = 1.284589287


Subproblem 2
x + 3.25 = -4.534589287

Simplifying
x + 3.25 = -4.534589287

Reorder the terms:
3.25 + x = -4.534589287

Solving
3.25 + x = -4.534589287

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 = -4.534589287 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = -4.534589287 + -3.25
x = -4.534589287 + -3.25

Combine like terms: -4.534589287 + -3.25 = -7.784589287
x = -7.784589287

Simplifying
x = -7.784589287


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.284589287, -7.784589287}

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