-16x^2+127x-175=0

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Solution for -16x^2+127x-175=0 equation: 


Simplifying
-16x2 + 127x + -175 = 0

Reorder the terms:
-175 + 127x + -16x2 = 0

Solving
-175 + 127x + -16x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
10.9375 + -7.9375x + x2 = 0

Move the constant term to the right:

Add '-10.9375' to each side of the equation.
10.9375 + -7.9375x + -10.9375 + x2 = 0 + -10.9375

Reorder the terms:
10.9375 + -10.9375 + -7.9375x + x2 = 0 + -10.9375

Combine like terms: 10.9375 + -10.9375 = 0.0000
0.0000 + -7.9375x + x2 = 0 + -10.9375
-7.9375x + x2 = 0 + -10.9375

Combine like terms: 0 + -10.9375 = -10.9375
-7.9375x + x2 = -10.9375

The x term is -7.9375x.  Take half its coefficient (-3.96875).
Square it (15.75097656) and add it to both sides.

Add '15.75097656' to each side of the equation.
-7.9375x + 15.75097656 + x2 = -10.9375 + 15.75097656

Reorder the terms:
15.75097656 + -7.9375x + x2 = -10.9375 + 15.75097656

Combine like terms: -10.9375 + 15.75097656 = 4.81347656
15.75097656 + -7.9375x + x2 = 4.81347656

Factor a perfect square on the left side:
(x + -3.96875)(x + -3.96875) = 4.81347656

Calculate the square root of the right side: 2.193963664

Break this problem into two subproblems by setting 
(x + -3.96875) equal to 2.193963664 and -2.193963664.


Subproblem 1
x + -3.96875 = 2.193963664

Simplifying
x + -3.96875 = 2.193963664

Reorder the terms:
-3.96875 + x = 2.193963664

Solving
-3.96875 + x = 2.193963664

Solving for variable 'x'.

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

Add '3.96875' to each side of the equation.
-3.96875 + 3.96875 + x = 2.193963664 + 3.96875

Combine like terms: -3.96875 + 3.96875 = 0.00000
0.00000 + x = 2.193963664 + 3.96875
x = 2.193963664 + 3.96875

Combine like terms: 2.193963664 + 3.96875 = 6.162713664
x = 6.162713664

Simplifying
x = 6.162713664


Subproblem 2
x + -3.96875 = -2.193963664

Simplifying
x + -3.96875 = -2.193963664

Reorder the terms:
-3.96875 + x = -2.193963664

Solving
-3.96875 + x = -2.193963664

Solving for variable 'x'.

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

Add '3.96875' to each side of the equation.
-3.96875 + 3.96875 + x = -2.193963664 + 3.96875

Combine like terms: -3.96875 + 3.96875 = 0.00000
0.00000 + x = -2.193963664 + 3.96875
x = -2.193963664 + 3.96875

Combine like terms: -2.193963664 + 3.96875 = 1.774786336
x = 1.774786336

Simplifying
x = 1.774786336


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.162713664, 1.774786336}

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