x(x+7)=26

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Solution for x(x+7)=26 equation: 


Simplifying
x(x + 7) = 26

Reorder the terms:
x(7 + x) = 26
(7 * x + x * x) = 26
(7x + x2) = 26

Solving
7x + x2 = 26

Solving for variable 'x'.

Reorder the terms:
-26 + 7x + x2 = 26 + -26

Combine like terms: 26 + -26 = 0
-26 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + 7x + 26 + x2 = 0 + 26

Reorder the terms:
-26 + 26 + 7x + x2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + 7x + x2 = 0 + 26
7x + x2 = 0 + 26

Combine like terms: 0 + 26 = 26
7x + x2 = 26

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 26 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 26 + 12.25

Combine like terms: 26 + 12.25 = 38.25
12.25 + 7x + x2 = 38.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(x + 3.5) equal to 6.184658438 and -6.184658438.


Subproblem 1
x + 3.5 = 6.184658438

Simplifying
x + 3.5 = 6.184658438

Reorder the terms:
3.5 + x = 6.184658438

Solving
3.5 + x = 6.184658438

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 6.184658438 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 6.184658438 + -3.5
x = 6.184658438 + -3.5

Combine like terms: 6.184658438 + -3.5 = 2.684658438
x = 2.684658438

Simplifying
x = 2.684658438


Subproblem 2
x + 3.5 = -6.184658438

Simplifying
x + 3.5 = -6.184658438

Reorder the terms:
3.5 + x = -6.184658438

Solving
3.5 + x = -6.184658438

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -6.184658438 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -6.184658438 + -3.5
x = -6.184658438 + -3.5

Combine like terms: -6.184658438 + -3.5 = -9.684658438
x = -9.684658438

Simplifying
x = -9.684658438


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.684658438, -9.684658438}

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