4x(4x+9)=225

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Solution for 4x(4x+9)=225 equation: 


Simplifying
4x(4x + 9) = 225

Reorder the terms:
4x(9 + 4x) = 225
(9 * 4x + 4x * 4x) = 225
(36x + 16x2) = 225

Solving
36x + 16x2 = 225

Solving for variable 'x'.

Reorder the terms:
-225 + 36x + 16x2 = 225 + -225

Combine like terms: 225 + -225 = 0
-225 + 36x + 16x2 = 0

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

Divide each side by '16'.
-14.0625 + 2.25x + x2 = 0

Move the constant term to the right:

Add '14.0625' to each side of the equation.
-14.0625 + 2.25x + 14.0625 + x2 = 0 + 14.0625

Reorder the terms:
-14.0625 + 14.0625 + 2.25x + x2 = 0 + 14.0625

Combine like terms: -14.0625 + 14.0625 = 0.0000
0.0000 + 2.25x + x2 = 0 + 14.0625
2.25x + x2 = 0 + 14.0625

Combine like terms: 0 + 14.0625 = 14.0625
2.25x + x2 = 14.0625

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 = 14.0625 + 1.265625

Reorder the terms:
1.265625 + 2.25x + x2 = 14.0625 + 1.265625

Combine like terms: 14.0625 + 1.265625 = 15.328125
1.265625 + 2.25x + x2 = 15.328125

Factor a perfect square on the left side:
(x + 1.125)(x + 1.125) = 15.328125

Calculate the square root of the right side: 3.915114941

Break this problem into two subproblems by setting 
(x + 1.125) equal to 3.915114941 and -3.915114941.


Subproblem 1
x + 1.125 = 3.915114941

Simplifying
x + 1.125 = 3.915114941

Reorder the terms:
1.125 + x = 3.915114941

Solving
1.125 + x = 3.915114941

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 = 3.915114941 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = 3.915114941 + -1.125
x = 3.915114941 + -1.125

Combine like terms: 3.915114941 + -1.125 = 2.790114941
x = 2.790114941

Simplifying
x = 2.790114941


Subproblem 2
x + 1.125 = -3.915114941

Simplifying
x + 1.125 = -3.915114941

Reorder the terms:
1.125 + x = -3.915114941

Solving
1.125 + x = -3.915114941

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 = -3.915114941 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = -3.915114941 + -1.125
x = -3.915114941 + -1.125

Combine like terms: -3.915114941 + -1.125 = -5.040114941
x = -5.040114941

Simplifying
x = -5.040114941


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.790114941, -5.040114941}

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