x(x+3)=201

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Solution for x(x+3)=201 equation: 


Simplifying
x(x + 3) = 201

Reorder the terms:
x(3 + x) = 201
(3 * x + x * x) = 201
(3x + x2) = 201

Solving
3x + x2 = 201

Solving for variable 'x'.

Reorder the terms:
-201 + 3x + x2 = 201 + -201

Combine like terms: 201 + -201 = 0
-201 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '201' to each side of the equation.
-201 + 3x + 201 + x2 = 0 + 201

Reorder the terms:
-201 + 201 + 3x + x2 = 0 + 201

Combine like terms: -201 + 201 = 0
0 + 3x + x2 = 0 + 201
3x + x2 = 0 + 201

Combine like terms: 0 + 201 = 201
3x + x2 = 201

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 201 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 201 + 2.25

Combine like terms: 201 + 2.25 = 203.25
2.25 + 3x + x2 = 203.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 203.25

Calculate the square root of the right side: 14.256577429

Break this problem into two subproblems by setting 
(x + 1.5) equal to 14.256577429 and -14.256577429.


Subproblem 1
x + 1.5 = 14.256577429

Simplifying
x + 1.5 = 14.256577429

Reorder the terms:
1.5 + x = 14.256577429

Solving
1.5 + x = 14.256577429

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 14.256577429 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 14.256577429 + -1.5
x = 14.256577429 + -1.5

Combine like terms: 14.256577429 + -1.5 = 12.756577429
x = 12.756577429

Simplifying
x = 12.756577429


Subproblem 2
x + 1.5 = -14.256577429

Simplifying
x + 1.5 = -14.256577429

Reorder the terms:
1.5 + x = -14.256577429

Solving
1.5 + x = -14.256577429

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -14.256577429 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -14.256577429 + -1.5
x = -14.256577429 + -1.5

Combine like terms: -14.256577429 + -1.5 = -15.756577429
x = -15.756577429

Simplifying
x = -15.756577429


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.756577429, -15.756577429}

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