x(x+7)=1600

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Solution for x(x+7)=1600 equation: 


Simplifying
x(x + 7) = 1600

Reorder the terms:
x(7 + x) = 1600
(7 * x + x * x) = 1600
(7x + x2) = 1600

Solving
7x + x2 = 1600

Solving for variable 'x'.

Reorder the terms:
-1600 + 7x + x2 = 1600 + -1600

Combine like terms: 1600 + -1600 = 0
-1600 + 7x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1600' to each side of the equation.
-1600 + 7x + 1600 + x2 = 0 + 1600

Reorder the terms:
-1600 + 1600 + 7x + x2 = 0 + 1600

Combine like terms: -1600 + 1600 = 0
0 + 7x + x2 = 0 + 1600
7x + x2 = 0 + 1600

Combine like terms: 0 + 1600 = 1600
7x + x2 = 1600

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 = 1600 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 1600 + 12.25

Combine like terms: 1600 + 12.25 = 1612.25
12.25 + 7x + x2 = 1612.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 1612.25

Calculate the square root of the right side: 40.152833026

Break this problem into two subproblems by setting 
(x + 3.5) equal to 40.152833026 and -40.152833026.


Subproblem 1
x + 3.5 = 40.152833026

Simplifying
x + 3.5 = 40.152833026

Reorder the terms:
3.5 + x = 40.152833026

Solving
3.5 + x = 40.152833026

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 = 40.152833026 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 40.152833026 + -3.5
x = 40.152833026 + -3.5

Combine like terms: 40.152833026 + -3.5 = 36.652833026
x = 36.652833026

Simplifying
x = 36.652833026


Subproblem 2
x + 3.5 = -40.152833026

Simplifying
x + 3.5 = -40.152833026

Reorder the terms:
3.5 + x = -40.152833026

Solving
3.5 + x = -40.152833026

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 = -40.152833026 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -40.152833026 + -3.5
x = -40.152833026 + -3.5

Combine like terms: -40.152833026 + -3.5 = -43.652833026
x = -43.652833026

Simplifying
x = -43.652833026


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {36.652833026, -43.652833026}

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