4x^2-63x-157=0

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Solution for 4x^2-63x-157=0 equation: 


Simplifying
4x2 + -63x + -157 = 0

Reorder the terms:
-157 + -63x + 4x2 = 0

Solving
-157 + -63x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-39.25 + -15.75x + x2 = 0

Move the constant term to the right:

Add '39.25' to each side of the equation.
-39.25 + -15.75x + 39.25 + x2 = 0 + 39.25

Reorder the terms:
-39.25 + 39.25 + -15.75x + x2 = 0 + 39.25

Combine like terms: -39.25 + 39.25 = 0.00
0.00 + -15.75x + x2 = 0 + 39.25
-15.75x + x2 = 0 + 39.25

Combine like terms: 0 + 39.25 = 39.25
-15.75x + x2 = 39.25

The x term is -15.75x.  Take half its coefficient (-7.875).
Square it (62.015625) and add it to both sides.

Add '62.015625' to each side of the equation.
-15.75x + 62.015625 + x2 = 39.25 + 62.015625

Reorder the terms:
62.015625 + -15.75x + x2 = 39.25 + 62.015625

Combine like terms: 39.25 + 62.015625 = 101.265625
62.015625 + -15.75x + x2 = 101.265625

Factor a perfect square on the left side:
(x + -7.875)(x + -7.875) = 101.265625

Calculate the square root of the right side: 10.063082281

Break this problem into two subproblems by setting 
(x + -7.875) equal to 10.063082281 and -10.063082281.


Subproblem 1
x + -7.875 = 10.063082281

Simplifying
x + -7.875 = 10.063082281

Reorder the terms:
-7.875 + x = 10.063082281

Solving
-7.875 + x = 10.063082281

Solving for variable 'x'.

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

Add '7.875' to each side of the equation.
-7.875 + 7.875 + x = 10.063082281 + 7.875

Combine like terms: -7.875 + 7.875 = 0.000
0.000 + x = 10.063082281 + 7.875
x = 10.063082281 + 7.875

Combine like terms: 10.063082281 + 7.875 = 17.938082281
x = 17.938082281

Simplifying
x = 17.938082281


Subproblem 2
x + -7.875 = -10.063082281

Simplifying
x + -7.875 = -10.063082281

Reorder the terms:
-7.875 + x = -10.063082281

Solving
-7.875 + x = -10.063082281

Solving for variable 'x'.

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

Add '7.875' to each side of the equation.
-7.875 + 7.875 + x = -10.063082281 + 7.875

Combine like terms: -7.875 + 7.875 = 0.000
0.000 + x = -10.063082281 + 7.875
x = -10.063082281 + 7.875

Combine like terms: -10.063082281 + 7.875 = -2.188082281
x = -2.188082281

Simplifying
x = -2.188082281


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.938082281, -2.188082281}

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