2x(4x+9)=20

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Solution for 2x(4x+9)=20 equation: 


Simplifying
2x(4x + 9) = 20

Reorder the terms:
2x(9 + 4x) = 20
(9 * 2x + 4x * 2x) = 20
(18x + 8x2) = 20

Solving
18x + 8x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + 18x + 8x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 18x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 9x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-10 + 9x + 4x2)' equal to zero and attempt to solve:

Simplifying
-10 + 9x + 4x2 = 0

Solving
-10 + 9x + 4x2 = 0

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

Divide each side by '4'.
-2.5 + 2.25x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 2.25x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 2.25x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 2.25x + x2 = 0 + 2.5
2.25x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
2.25x + x2 = 2.5

The x term is 2.25x.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25x + 1.265625 + x2 = 2.5 + 1.265625

Reorder the terms:
1.265625 + 2.25x + x2 = 2.5 + 1.265625

Combine like terms: 2.5 + 1.265625 = 3.765625
1.265625 + 2.25x + x2 = 3.765625

Factor a perfect square on the left side:
(x + 1.125)(x + 1.125) = 3.765625

Calculate the square root of the right side: 1.940521837

Break this problem into two subproblems by setting 
(x + 1.125) equal to 1.940521837 and -1.940521837.


Subproblem 1
x + 1.125 = 1.940521837

Simplifying
x + 1.125 = 1.940521837

Reorder the terms:
1.125 + x = 1.940521837

Solving
1.125 + x = 1.940521837

Solving for variable 'x'.

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

Add '-1.125' to each side of the equation.
1.125 + -1.125 + x = 1.940521837 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = 1.940521837 + -1.125
x = 1.940521837 + -1.125

Combine like terms: 1.940521837 + -1.125 = 0.815521837
x = 0.815521837

Simplifying
x = 0.815521837


Subproblem 2
x + 1.125 = -1.940521837

Simplifying
x + 1.125 = -1.940521837

Reorder the terms:
1.125 + x = -1.940521837

Solving
1.125 + x = -1.940521837

Solving for variable 'x'.

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

Add '-1.125' to each side of the equation.
1.125 + -1.125 + x = -1.940521837 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = -1.940521837 + -1.125
x = -1.940521837 + -1.125

Combine like terms: -1.940521837 + -1.125 = -3.065521837
x = -3.065521837

Simplifying
x = -3.065521837


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.815521837, -3.065521837}
Solution
x = {0.815521837, -3.065521837}

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