x(x+7)=36.75

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Solution for x(x+7)=36.75 equation: 


Simplifying
x(x + 7) = 36.75

Reorder the terms:
x(7 + x) = 36.75
(7 * x + x * x) = 36.75
(7x + x2) = 36.75

Solving
7x + x2 = 36.75

Solving for variable 'x'.

Reorder the terms:
-36.75 + 7x + x2 = 36.75 + -36.75

Combine like terms: 36.75 + -36.75 = 0.00
-36.75 + 7x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '36.75' to each side of the equation.
-36.75 + 7x + 36.75 + x2 = 0.00 + 36.75

Reorder the terms:
-36.75 + 36.75 + 7x + x2 = 0.00 + 36.75

Combine like terms: -36.75 + 36.75 = 0.00
0.00 + 7x + x2 = 0.00 + 36.75
7x + x2 = 0.00 + 36.75

Combine like terms: 0.00 + 36.75 = 36.75
7x + x2 = 36.75

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 = 36.75 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 36.75 + 12.25

Combine like terms: 36.75 + 12.25 = 49
12.25 + 7x + x2 = 49

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 49

Calculate the square root of the right side: 7

Break this problem into two subproblems by setting 
(x + 3.5) equal to 7 and -7.


Subproblem 1
x + 3.5 = 7

Simplifying
x + 3.5 = 7

Reorder the terms:
3.5 + x = 7

Solving
3.5 + x = 7

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 = 7 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 7 + -3.5
x = 7 + -3.5

Combine like terms: 7 + -3.5 = 3.5
x = 3.5

Simplifying
x = 3.5


Subproblem 2
x + 3.5 = -7

Simplifying
x + 3.5 = -7

Reorder the terms:
3.5 + x = -7

Solving
3.5 + x = -7

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 = -7 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -7 + -3.5
x = -7 + -3.5

Combine like terms: -7 + -3.5 = -10.5
x = -10.5

Simplifying
x = -10.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.5, -10.5}

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