x(7+x)=130

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Solution for x(7+x)=130 equation: 


Simplifying
x(7 + x) = 130
(7 * x + x * x) = 130
(7x + x2) = 130

Solving
7x + x2 = 130

Solving for variable 'x'.

Reorder the terms:
-130 + 7x + x2 = 130 + -130

Combine like terms: 130 + -130 = 0
-130 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '130' to each side of the equation.
-130 + 7x + 130 + x2 = 0 + 130

Reorder the terms:
-130 + 130 + 7x + x2 = 0 + 130

Combine like terms: -130 + 130 = 0
0 + 7x + x2 = 0 + 130
7x + x2 = 0 + 130

Combine like terms: 0 + 130 = 130
7x + x2 = 130

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 = 130 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 130 + 12.25

Combine like terms: 130 + 12.25 = 142.25
12.25 + 7x + x2 = 142.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 142.25

Calculate the square root of the right side: 11.926860442

Break this problem into two subproblems by setting 
(x + 3.5) equal to 11.926860442 and -11.926860442.


Subproblem 1
x + 3.5 = 11.926860442

Simplifying
x + 3.5 = 11.926860442

Reorder the terms:
3.5 + x = 11.926860442

Solving
3.5 + x = 11.926860442

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 = 11.926860442 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 11.926860442 + -3.5
x = 11.926860442 + -3.5

Combine like terms: 11.926860442 + -3.5 = 8.426860442
x = 8.426860442

Simplifying
x = 8.426860442


Subproblem 2
x + 3.5 = -11.926860442

Simplifying
x + 3.5 = -11.926860442

Reorder the terms:
3.5 + x = -11.926860442

Solving
3.5 + x = -11.926860442

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 = -11.926860442 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -11.926860442 + -3.5
x = -11.926860442 + -3.5

Combine like terms: -11.926860442 + -3.5 = -15.426860442
x = -15.426860442

Simplifying
x = -15.426860442


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.426860442, -15.426860442}

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