(4x+9)(4x+9)+25=0

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Solution for (4x+9)(4x+9)+25=0 equation: 


Simplifying
(4x + 9)(4x + 9) + 25 = 0

Reorder the terms:
(9 + 4x)(4x + 9) + 25 = 0

Reorder the terms:
(9 + 4x)(9 + 4x) + 25 = 0

Multiply (9 + 4x) * (9 + 4x)
(9(9 + 4x) + 4x * (9 + 4x)) + 25 = 0
((9 * 9 + 4x * 9) + 4x * (9 + 4x)) + 25 = 0
((81 + 36x) + 4x * (9 + 4x)) + 25 = 0
(81 + 36x + (9 * 4x + 4x * 4x)) + 25 = 0
(81 + 36x + (36x + 16x2)) + 25 = 0

Combine like terms: 36x + 36x = 72x
(81 + 72x + 16x2) + 25 = 0

Reorder the terms:
81 + 25 + 72x + 16x2 = 0

Combine like terms: 81 + 25 = 106
106 + 72x + 16x2 = 0

Solving
106 + 72x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(53 + 36x + 8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(53 + 36x + 8x2)' equal to zero and attempt to solve:

Simplifying
53 + 36x + 8x2 = 0

Solving
53 + 36x + 8x2 = 0

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

Divide each side by '8'.
6.625 + 4.5x + x2 = 0

Move the constant term to the right:

Add '-6.625' to each side of the equation.
6.625 + 4.5x + -6.625 + x2 = 0 + -6.625

Reorder the terms:
6.625 + -6.625 + 4.5x + x2 = 0 + -6.625

Combine like terms: 6.625 + -6.625 = 0.000
0.000 + 4.5x + x2 = 0 + -6.625
4.5x + x2 = 0 + -6.625

Combine like terms: 0 + -6.625 = -6.625
4.5x + x2 = -6.625

The x term is 4.5x.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5x + 5.0625 + x2 = -6.625 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = -6.625 + 5.0625

Combine like terms: -6.625 + 5.0625 = -1.5625
5.0625 + 4.5x + x2 = -1.5625

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = -1.5625

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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