7x^2-5x-64=0

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Solution for 7x^2-5x-64=0 equation: 


Simplifying
7x2 + -5x + -64 = 0

Reorder the terms:
-64 + -5x + 7x2 = 0

Solving
-64 + -5x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-9.142857143 + -0.7142857143x + x2 = 0

Move the constant term to the right:

Add '9.142857143' to each side of the equation.
-9.142857143 + -0.7142857143x + 9.142857143 + x2 = 0 + 9.142857143

Reorder the terms:
-9.142857143 + 9.142857143 + -0.7142857143x + x2 = 0 + 9.142857143

Combine like terms: -9.142857143 + 9.142857143 = 0.000000000
0.000000000 + -0.7142857143x + x2 = 0 + 9.142857143
-0.7142857143x + x2 = 0 + 9.142857143

Combine like terms: 0 + 9.142857143 = 9.142857143
-0.7142857143x + x2 = 9.142857143

The x term is -0.7142857143x.  Take half its coefficient (-0.3571428572).
Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.
-0.7142857143x + 0.1275510204 + x2 = 9.142857143 + 0.1275510204

Reorder the terms:
0.1275510204 + -0.7142857143x + x2 = 9.142857143 + 0.1275510204

Combine like terms: 9.142857143 + 0.1275510204 = 9.2704081634
0.1275510204 + -0.7142857143x + x2 = 9.2704081634

Factor a perfect square on the left side:
(x + -0.3571428572)(x + -0.3571428572) = 9.2704081634

Calculate the square root of the right side: 3.044734498

Break this problem into two subproblems by setting 
(x + -0.3571428572) equal to 3.044734498 and -3.044734498.


Subproblem 1
x + -0.3571428572 = 3.044734498

Simplifying
x + -0.3571428572 = 3.044734498

Reorder the terms:
-0.3571428572 + x = 3.044734498

Solving
-0.3571428572 + x = 3.044734498

Solving for variable 'x'.

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

Add '0.3571428572' to each side of the equation.
-0.3571428572 + 0.3571428572 + x = 3.044734498 + 0.3571428572

Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000
0.0000000000 + x = 3.044734498 + 0.3571428572
x = 3.044734498 + 0.3571428572

Combine like terms: 3.044734498 + 0.3571428572 = 3.4018773552
x = 3.4018773552

Simplifying
x = 3.4018773552


Subproblem 2
x + -0.3571428572 = -3.044734498

Simplifying
x + -0.3571428572 = -3.044734498

Reorder the terms:
-0.3571428572 + x = -3.044734498

Solving
-0.3571428572 + x = -3.044734498

Solving for variable 'x'.

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

Add '0.3571428572' to each side of the equation.
-0.3571428572 + 0.3571428572 + x = -3.044734498 + 0.3571428572

Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000
0.0000000000 + x = -3.044734498 + 0.3571428572
x = -3.044734498 + 0.3571428572

Combine like terms: -3.044734498 + 0.3571428572 = -2.6875916408
x = -2.6875916408

Simplifying
x = -2.6875916408


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.4018773552, -2.6875916408}

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