7x^2-28x-64=0

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Solution for 7x^2-28x-64=0 equation: 


Simplifying
7x2 + -28x + -64 = 0

Reorder the terms:
-64 + -28x + 7x2 = 0

Solving
-64 + -28x + 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 + -4x + x2 = 0

Move the constant term to the right:

Add '9.142857143' to each side of the equation.
-9.142857143 + -4x + 9.142857143 + x2 = 0 + 9.142857143

Reorder the terms:
-9.142857143 + 9.142857143 + -4x + x2 = 0 + 9.142857143

Combine like terms: -9.142857143 + 9.142857143 = 0.000000000
0.000000000 + -4x + x2 = 0 + 9.142857143
-4x + x2 = 0 + 9.142857143

Combine like terms: 0 + 9.142857143 = 9.142857143
-4x + x2 = 9.142857143

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 9.142857143 + 4

Reorder the terms:
4 + -4x + x2 = 9.142857143 + 4

Combine like terms: 9.142857143 + 4 = 13.142857143
4 + -4x + x2 = 13.142857143

Factor a perfect square on the left side:
(x + -2)(x + -2) = 13.142857143

Calculate the square root of the right side: 3.625307869

Break this problem into two subproblems by setting 
(x + -2) equal to 3.625307869 and -3.625307869.


Subproblem 1
x + -2 = 3.625307869

Simplifying
x + -2 = 3.625307869

Reorder the terms:
-2 + x = 3.625307869

Solving
-2 + x = 3.625307869

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 3.625307869 + 2

Combine like terms: -2 + 2 = 0
0 + x = 3.625307869 + 2
x = 3.625307869 + 2

Combine like terms: 3.625307869 + 2 = 5.625307869
x = 5.625307869

Simplifying
x = 5.625307869


Subproblem 2
x + -2 = -3.625307869

Simplifying
x + -2 = -3.625307869

Reorder the terms:
-2 + x = -3.625307869

Solving
-2 + x = -3.625307869

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -3.625307869 + 2

Combine like terms: -2 + 2 = 0
0 + x = -3.625307869 + 2
x = -3.625307869 + 2

Combine like terms: -3.625307869 + 2 = -1.625307869
x = -1.625307869

Simplifying
x = -1.625307869


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.625307869, -1.625307869}

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