(x+3)2x-6=2600

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Solution for (x+3)2x-6=2600 equation: 


Simplifying
(x + 3) * 2x + -6 = 2600

Reorder the terms:
(3 + x) * 2x + -6 = 2600

Reorder the terms for easier multiplication:
2x(3 + x) + -6 = 2600
(3 * 2x + x * 2x) + -6 = 2600
(6x + 2x2) + -6 = 2600

Reorder the terms:
-6 + 6x + 2x2 = 2600

Solving
-6 + 6x + 2x2 = 2600

Solving for variable 'x'.

Reorder the terms:
-6 + -2600 + 6x + 2x2 = 2600 + -2600

Combine like terms: -6 + -2600 = -2606
-2606 + 6x + 2x2 = 2600 + -2600

Combine like terms: 2600 + -2600 = 0
-2606 + 6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1303 + 3x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1303 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
-1303 + 3x + x2 = 0

Solving
-1303 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1303' to each side of the equation.
-1303 + 3x + 1303 + x2 = 0 + 1303

Reorder the terms:
-1303 + 1303 + 3x + x2 = 0 + 1303

Combine like terms: -1303 + 1303 = 0
0 + 3x + x2 = 0 + 1303
3x + x2 = 0 + 1303

Combine like terms: 0 + 1303 = 1303
3x + x2 = 1303

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 1303 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 1303 + 2.25

Combine like terms: 1303 + 2.25 = 1305.25
2.25 + 3x + x2 = 1305.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 1305.25

Calculate the square root of the right side: 36.128243799

Break this problem into two subproblems by setting 
(x + 1.5) equal to 36.128243799 and -36.128243799.


Subproblem 1
x + 1.5 = 36.128243799

Simplifying
x + 1.5 = 36.128243799

Reorder the terms:
1.5 + x = 36.128243799

Solving
1.5 + x = 36.128243799

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 36.128243799 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 36.128243799 + -1.5
x = 36.128243799 + -1.5

Combine like terms: 36.128243799 + -1.5 = 34.628243799
x = 34.628243799

Simplifying
x = 34.628243799


Subproblem 2
x + 1.5 = -36.128243799

Simplifying
x + 1.5 = -36.128243799

Reorder the terms:
1.5 + x = -36.128243799

Solving
1.5 + x = -36.128243799

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -36.128243799 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -36.128243799 + -1.5
x = -36.128243799 + -1.5

Combine like terms: -36.128243799 + -1.5 = -37.628243799
x = -37.628243799

Simplifying
x = -37.628243799


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {34.628243799, -37.628243799}
Solution
x = {34.628243799, -37.628243799}

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