x(x+3)=24

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Solution for x(x+3)=24 equation: 


Simplifying
x(x + 3) = 24

Reorder the terms:
x(3 + x) = 24
(3 * x + x * x) = 24
(3x + x2) = 24

Solving
3x + x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + 3x + x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 3x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 3x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 3x + x2 = 0 + 24
3x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
3x + x2 = 24

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 = 24 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 24 + 2.25

Combine like terms: 24 + 2.25 = 26.25
2.25 + 3x + x2 = 26.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(x + 1.5) equal to 5.123475383 and -5.123475383.


Subproblem 1
x + 1.5 = 5.123475383

Simplifying
x + 1.5 = 5.123475383

Reorder the terms:
1.5 + x = 5.123475383

Solving
1.5 + x = 5.123475383

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 = 5.123475383 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 5.123475383 + -1.5
x = 5.123475383 + -1.5

Combine like terms: 5.123475383 + -1.5 = 3.623475383
x = 3.623475383

Simplifying
x = 3.623475383


Subproblem 2
x + 1.5 = -5.123475383

Simplifying
x + 1.5 = -5.123475383

Reorder the terms:
1.5 + x = -5.123475383

Solving
1.5 + x = -5.123475383

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 = -5.123475383 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -5.123475383 + -1.5
x = -5.123475383 + -1.5

Combine like terms: -5.123475383 + -1.5 = -6.623475383
x = -6.623475383

Simplifying
x = -6.623475383


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.623475383, -6.623475383}

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