7x^2-66x-48=0

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Solution for 7x^2-66x-48=0 equation: 


Simplifying
7x2 + -66x + -48 = 0

Reorder the terms:
-48 + -66x + 7x2 = 0

Solving
-48 + -66x + 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'.
-6.857142857 + -9.428571429x + x2 = 0

Move the constant term to the right:

Add '6.857142857' to each side of the equation.
-6.857142857 + -9.428571429x + 6.857142857 + x2 = 0 + 6.857142857

Reorder the terms:
-6.857142857 + 6.857142857 + -9.428571429x + x2 = 0 + 6.857142857

Combine like terms: -6.857142857 + 6.857142857 = 0.000000000
0.000000000 + -9.428571429x + x2 = 0 + 6.857142857
-9.428571429x + x2 = 0 + 6.857142857

Combine like terms: 0 + 6.857142857 = 6.857142857
-9.428571429x + x2 = 6.857142857

The x term is -9.428571429x.  Take half its coefficient (-4.714285715).
Square it (22.22448980) and add it to both sides.

Add '22.22448980' to each side of the equation.
-9.428571429x + 22.22448980 + x2 = 6.857142857 + 22.22448980

Reorder the terms:
22.22448980 + -9.428571429x + x2 = 6.857142857 + 22.22448980

Combine like terms: 6.857142857 + 22.22448980 = 29.081632657
22.22448980 + -9.428571429x + x2 = 29.081632657

Factor a perfect square on the left side:
(x + -4.714285715)(x + -4.714285715) = 29.081632657

Calculate the square root of the right side: 5.392738883

Break this problem into two subproblems by setting 
(x + -4.714285715) equal to 5.392738883 and -5.392738883.


Subproblem 1
x + -4.714285715 = 5.392738883

Simplifying
x + -4.714285715 = 5.392738883

Reorder the terms:
-4.714285715 + x = 5.392738883

Solving
-4.714285715 + x = 5.392738883

Solving for variable 'x'.

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

Add '4.714285715' to each side of the equation.
-4.714285715 + 4.714285715 + x = 5.392738883 + 4.714285715

Combine like terms: -4.714285715 + 4.714285715 = 0.000000000
0.000000000 + x = 5.392738883 + 4.714285715
x = 5.392738883 + 4.714285715

Combine like terms: 5.392738883 + 4.714285715 = 10.107024598
x = 10.107024598

Simplifying
x = 10.107024598


Subproblem 2
x + -4.714285715 = -5.392738883

Simplifying
x + -4.714285715 = -5.392738883

Reorder the terms:
-4.714285715 + x = -5.392738883

Solving
-4.714285715 + x = -5.392738883

Solving for variable 'x'.

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

Add '4.714285715' to each side of the equation.
-4.714285715 + 4.714285715 + x = -5.392738883 + 4.714285715

Combine like terms: -4.714285715 + 4.714285715 = 0.000000000
0.000000000 + x = -5.392738883 + 4.714285715
x = -5.392738883 + 4.714285715

Combine like terms: -5.392738883 + 4.714285715 = -0.678453168
x = -0.678453168

Simplifying
x = -0.678453168


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.107024598, -0.678453168}

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