9x^2+64x+64=0

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Solution for 9x^2+64x+64=0 equation: 


Simplifying
9x2 + 64x + 64 = 0

Reorder the terms:
64 + 64x + 9x2 = 0

Solving
64 + 64x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
7.111111111 + 7.111111111x + x2 = 0

Move the constant term to the right:

Add '-7.111111111' to each side of the equation.
7.111111111 + 7.111111111x + -7.111111111 + x2 = 0 + -7.111111111

Reorder the terms:
7.111111111 + -7.111111111 + 7.111111111x + x2 = 0 + -7.111111111

Combine like terms: 7.111111111 + -7.111111111 = 0.000000000
0.000000000 + 7.111111111x + x2 = 0 + -7.111111111
7.111111111x + x2 = 0 + -7.111111111

Combine like terms: 0 + -7.111111111 = -7.111111111
7.111111111x + x2 = -7.111111111

The x term is 7.111111111x.  Take half its coefficient (3.555555556).
Square it (12.64197531) and add it to both sides.

Add '12.64197531' to each side of the equation.
7.111111111x + 12.64197531 + x2 = -7.111111111 + 12.64197531

Reorder the terms:
12.64197531 + 7.111111111x + x2 = -7.111111111 + 12.64197531

Combine like terms: -7.111111111 + 12.64197531 = 5.530864199
12.64197531 + 7.111111111x + x2 = 5.530864199

Factor a perfect square on the left side:
(x + 3.555555556)(x + 3.555555556) = 5.530864199

Calculate the square root of the right side: 2.351778943

Break this problem into two subproblems by setting 
(x + 3.555555556) equal to 2.351778943 and -2.351778943.


Subproblem 1
x + 3.555555556 = 2.351778943

Simplifying
x + 3.555555556 = 2.351778943

Reorder the terms:
3.555555556 + x = 2.351778943

Solving
3.555555556 + x = 2.351778943

Solving for variable 'x'.

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

Add '-3.555555556' to each side of the equation.
3.555555556 + -3.555555556 + x = 2.351778943 + -3.555555556

Combine like terms: 3.555555556 + -3.555555556 = 0.000000000
0.000000000 + x = 2.351778943 + -3.555555556
x = 2.351778943 + -3.555555556

Combine like terms: 2.351778943 + -3.555555556 = -1.203776613
x = -1.203776613

Simplifying
x = -1.203776613


Subproblem 2
x + 3.555555556 = -2.351778943

Simplifying
x + 3.555555556 = -2.351778943

Reorder the terms:
3.555555556 + x = -2.351778943

Solving
3.555555556 + x = -2.351778943

Solving for variable 'x'.

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

Add '-3.555555556' to each side of the equation.
3.555555556 + -3.555555556 + x = -2.351778943 + -3.555555556

Combine like terms: 3.555555556 + -3.555555556 = 0.000000000
0.000000000 + x = -2.351778943 + -3.555555556
x = -2.351778943 + -3.555555556

Combine like terms: -2.351778943 + -3.555555556 = -5.907334499
x = -5.907334499

Simplifying
x = -5.907334499


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.203776613, -5.907334499}

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