(9x-5)(9x-5)=-78

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Solution for (9x-5)(9x-5)=-78 equation:


Simplifying
(9x + -5)(9x + -5) = -78

Reorder the terms:
(-5 + 9x)(9x + -5) = -78

Reorder the terms:
(-5 + 9x)(-5 + 9x) = -78

Multiply (-5 + 9x) * (-5 + 9x)
(-5(-5 + 9x) + 9x * (-5 + 9x)) = -78
((-5 * -5 + 9x * -5) + 9x * (-5 + 9x)) = -78
((25 + -45x) + 9x * (-5 + 9x)) = -78
(25 + -45x + (-5 * 9x + 9x * 9x)) = -78
(25 + -45x + (-45x + 81x2)) = -78

Combine like terms: -45x + -45x = -90x
(25 + -90x + 81x2) = -78

Solving
25 + -90x + 81x2 = -78

Solving for variable 'x'.

Reorder the terms:
25 + 78 + -90x + 81x2 = -78 + 78

Combine like terms: 25 + 78 = 103
103 + -90x + 81x2 = -78 + 78

Combine like terms: -78 + 78 = 0
103 + -90x + 81x2 = 0

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

Divide each side by '81'.
1.271604938 + -1.111111111x + x2 = 0

Move the constant term to the right:

Add '-1.271604938' to each side of the equation.
1.271604938 + -1.111111111x + -1.271604938 + x2 = 0 + -1.271604938

Reorder the terms:
1.271604938 + -1.271604938 + -1.111111111x + x2 = 0 + -1.271604938

Combine like terms: 1.271604938 + -1.271604938 = 0.000000000
0.000000000 + -1.111111111x + x2 = 0 + -1.271604938
-1.111111111x + x2 = 0 + -1.271604938

Combine like terms: 0 + -1.271604938 = -1.271604938
-1.111111111x + x2 = -1.271604938

The x term is -1.111111111x.  Take half its coefficient (-0.5555555555).
Square it (0.3086419752) and add it to both sides.

Add '0.3086419752' to each side of the equation.
-1.111111111x + 0.3086419752 + x2 = -1.271604938 + 0.3086419752

Reorder the terms:
0.3086419752 + -1.111111111x + x2 = -1.271604938 + 0.3086419752

Combine like terms: -1.271604938 + 0.3086419752 = -0.9629629628
0.3086419752 + -1.111111111x + x2 = -0.9629629628

Factor a perfect square on the left side:
(x + -0.5555555555)(x + -0.5555555555) = -0.9629629628

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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