2x(10x+24)=180

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Solution for 2x(10x+24)=180 equation: 


Simplifying
2x(10x + 24) = 180

Reorder the terms:
2x(24 + 10x) = 180
(24 * 2x + 10x * 2x) = 180
(48x + 20x2) = 180

Solving
48x + 20x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 48x + 20x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 48x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-45 + 12x + 5x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-45 + 12x + 5x2)' equal to zero and attempt to solve:

Simplifying
-45 + 12x + 5x2 = 0

Solving
-45 + 12x + 5x2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-9 + 2.4x + x2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 2.4x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 2.4x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 2.4x + x2 = 0 + 9
2.4x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
2.4x + x2 = 9

The x term is 2.4x.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4x + 1.44 + x2 = 9 + 1.44

Reorder the terms:
1.44 + 2.4x + x2 = 9 + 1.44

Combine like terms: 9 + 1.44 = 10.44
1.44 + 2.4x + x2 = 10.44

Factor a perfect square on the left side:
(x + 1.2)(x + 1.2) = 10.44

Calculate the square root of the right side: 3.231098884

Break this problem into two subproblems by setting 
(x + 1.2) equal to 3.231098884 and -3.231098884.


Subproblem 1
x + 1.2 = 3.231098884

Simplifying
x + 1.2 = 3.231098884

Reorder the terms:
1.2 + x = 3.231098884

Solving
1.2 + x = 3.231098884

Solving for variable 'x'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + x = 3.231098884 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + x = 3.231098884 + -1.2
x = 3.231098884 + -1.2

Combine like terms: 3.231098884 + -1.2 = 2.031098884
x = 2.031098884

Simplifying
x = 2.031098884


Subproblem 2
x + 1.2 = -3.231098884

Simplifying
x + 1.2 = -3.231098884

Reorder the terms:
1.2 + x = -3.231098884

Solving
1.2 + x = -3.231098884

Solving for variable 'x'.

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

Add '-1.2' to each side of the equation.
1.2 + -1.2 + x = -3.231098884 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + x = -3.231098884 + -1.2
x = -3.231098884 + -1.2

Combine like terms: -3.231098884 + -1.2 = -4.431098884
x = -4.431098884

Simplifying
x = -4.431098884


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.031098884, -4.431098884}
Solution
x = {2.031098884, -4.431098884}

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