x(x+3)=120

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Solution for x(x+3)=120 equation: 


Simplifying
x(x + 3) = 120

Reorder the terms:
x(3 + x) = 120
(3 * x + x * x) = 120
(3x + x2) = 120

Solving
3x + x2 = 120

Solving for variable 'x'.

Reorder the terms:
-120 + 3x + x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + 3x + 120 + x2 = 0 + 120

Reorder the terms:
-120 + 120 + 3x + x2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + 3x + x2 = 0 + 120
3x + x2 = 0 + 120

Combine like terms: 0 + 120 = 120
3x + x2 = 120

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 = 120 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 120 + 2.25

Combine like terms: 120 + 2.25 = 122.25
2.25 + 3x + x2 = 122.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 122.25

Calculate the square root of the right side: 11.056672194

Break this problem into two subproblems by setting 
(x + 1.5) equal to 11.056672194 and -11.056672194.


Subproblem 1
x + 1.5 = 11.056672194

Simplifying
x + 1.5 = 11.056672194

Reorder the terms:
1.5 + x = 11.056672194

Solving
1.5 + x = 11.056672194

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 = 11.056672194 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 11.056672194 + -1.5
x = 11.056672194 + -1.5

Combine like terms: 11.056672194 + -1.5 = 9.556672194
x = 9.556672194

Simplifying
x = 9.556672194


Subproblem 2
x + 1.5 = -11.056672194

Simplifying
x + 1.5 = -11.056672194

Reorder the terms:
1.5 + x = -11.056672194

Solving
1.5 + x = -11.056672194

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 = -11.056672194 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -11.056672194 + -1.5
x = -11.056672194 + -1.5

Combine like terms: -11.056672194 + -1.5 = -12.556672194
x = -12.556672194

Simplifying
x = -12.556672194


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.556672194, -12.556672194}

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