3x(2x+10)=288

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Solution for 3x(2x+10)=288 equation: 


Simplifying
3x(2x + 10) = 288

Reorder the terms:
3x(10 + 2x) = 288
(10 * 3x + 2x * 3x) = 288
(30x + 6x2) = 288

Solving
30x + 6x2 = 288

Solving for variable 'x'.

Reorder the terms:
-288 + 30x + 6x2 = 288 + -288

Combine like terms: 288 + -288 = 0
-288 + 30x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-48 + 5x + x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-48 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-48 + 5x + x2 = 0

Solving
-48 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 5x + 48 + x2 = 0 + 48

Reorder the terms:
-48 + 48 + 5x + x2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 5x + x2 = 0 + 48
5x + x2 = 0 + 48

Combine like terms: 0 + 48 = 48
5x + x2 = 48

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 48 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 48 + 6.25

Combine like terms: 48 + 6.25 = 54.25
6.25 + 5x + x2 = 54.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 54.25

Calculate the square root of the right side: 7.365459931

Break this problem into two subproblems by setting 
(x + 2.5) equal to 7.365459931 and -7.365459931.


Subproblem 1
x + 2.5 = 7.365459931

Simplifying
x + 2.5 = 7.365459931

Reorder the terms:
2.5 + x = 7.365459931

Solving
2.5 + x = 7.365459931

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 7.365459931 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 7.365459931 + -2.5
x = 7.365459931 + -2.5

Combine like terms: 7.365459931 + -2.5 = 4.865459931
x = 4.865459931

Simplifying
x = 4.865459931


Subproblem 2
x + 2.5 = -7.365459931

Simplifying
x + 2.5 = -7.365459931

Reorder the terms:
2.5 + x = -7.365459931

Solving
2.5 + x = -7.365459931

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -7.365459931 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -7.365459931 + -2.5
x = -7.365459931 + -2.5

Combine like terms: -7.365459931 + -2.5 = -9.865459931
x = -9.865459931

Simplifying
x = -9.865459931


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.865459931, -9.865459931}
Solution
x = {4.865459931, -9.865459931}

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