(3Z+4)(3Z+4)+144=0

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Solution for (3Z+4)(3Z+4)+144=0 equation: 


Simplifying
(3Z + 4)(3Z + 4) + 144 = 0

Reorder the terms:
(4 + 3Z)(3Z + 4) + 144 = 0

Reorder the terms:
(4 + 3Z)(4 + 3Z) + 144 = 0

Multiply (4 + 3Z) * (4 + 3Z)
(4(4 + 3Z) + 3Z * (4 + 3Z)) + 144 = 0
((4 * 4 + 3Z * 4) + 3Z * (4 + 3Z)) + 144 = 0
((16 + 12Z) + 3Z * (4 + 3Z)) + 144 = 0
(16 + 12Z + (4 * 3Z + 3Z * 3Z)) + 144 = 0
(16 + 12Z + (12Z + 9Z2)) + 144 = 0

Combine like terms: 12Z + 12Z = 24Z
(16 + 24Z + 9Z2) + 144 = 0

Reorder the terms:
16 + 144 + 24Z + 9Z2 = 0

Combine like terms: 16 + 144 = 160
160 + 24Z + 9Z2 = 0

Solving
160 + 24Z + 9Z2 = 0

Solving for variable 'Z'.

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

Divide each side by '9'.
17.77777778 + 2.666666667Z + Z2 = 0

Move the constant term to the right:

Add '-17.77777778' to each side of the equation.
17.77777778 + 2.666666667Z + -17.77777778 + Z2 = 0 + -17.77777778

Reorder the terms:
17.77777778 + -17.77777778 + 2.666666667Z + Z2 = 0 + -17.77777778

Combine like terms: 17.77777778 + -17.77777778 = 0.00000000
0.00000000 + 2.666666667Z + Z2 = 0 + -17.77777778
2.666666667Z + Z2 = 0 + -17.77777778

Combine like terms: 0 + -17.77777778 = -17.77777778
2.666666667Z + Z2 = -17.77777778

The Z term is 2.666666667Z.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667Z + 1.777777780 + Z2 = -17.77777778 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667Z + Z2 = -17.77777778 + 1.777777780

Combine like terms: -17.77777778 + 1.777777780 = -16
1.777777780 + 2.666666667Z + Z2 = -16

Factor a perfect square on the left side:
(Z + 1.333333334)(Z + 1.333333334) = -16

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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