x(x+7)=80

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Solution for x(x+7)=80 equation: 


Simplifying
x(x + 7) = 80

Reorder the terms:
x(7 + x) = 80
(7 * x + x * x) = 80
(7x + x2) = 80

Solving
7x + x2 = 80

Solving for variable 'x'.

Reorder the terms:
-80 + 7x + x2 = 80 + -80

Combine like terms: 80 + -80 = 0
-80 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + 7x + 80 + x2 = 0 + 80

Reorder the terms:
-80 + 80 + 7x + x2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + 7x + x2 = 0 + 80
7x + x2 = 0 + 80

Combine like terms: 0 + 80 = 80
7x + x2 = 80

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 = 80 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 80 + 12.25

Combine like terms: 80 + 12.25 = 92.25
12.25 + 7x + x2 = 92.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 92.25

Calculate the square root of the right side: 9.604686356

Break this problem into two subproblems by setting 
(x + 3.5) equal to 9.604686356 and -9.604686356.


Subproblem 1
x + 3.5 = 9.604686356

Simplifying
x + 3.5 = 9.604686356

Reorder the terms:
3.5 + x = 9.604686356

Solving
3.5 + x = 9.604686356

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 = 9.604686356 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 9.604686356 + -3.5
x = 9.604686356 + -3.5

Combine like terms: 9.604686356 + -3.5 = 6.104686356
x = 6.104686356

Simplifying
x = 6.104686356


Subproblem 2
x + 3.5 = -9.604686356

Simplifying
x + 3.5 = -9.604686356

Reorder the terms:
3.5 + x = -9.604686356

Solving
3.5 + x = -9.604686356

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 = -9.604686356 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -9.604686356 + -3.5
x = -9.604686356 + -3.5

Combine like terms: -9.604686356 + -3.5 = -13.104686356
x = -13.104686356

Simplifying
x = -13.104686356


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.104686356, -13.104686356}

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