-16x^2+215x-178=0

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Solution for -16x^2+215x-178=0 equation: 


Simplifying
-16x2 + 215x + -178 = 0

Reorder the terms:
-178 + 215x + -16x2 = 0

Solving
-178 + 215x + -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'.
11.125 + -13.4375x + x2 = 0

Move the constant term to the right:

Add '-11.125' to each side of the equation.
11.125 + -13.4375x + -11.125 + x2 = 0 + -11.125

Reorder the terms:
11.125 + -11.125 + -13.4375x + x2 = 0 + -11.125

Combine like terms: 11.125 + -11.125 = 0.000
0.000 + -13.4375x + x2 = 0 + -11.125
-13.4375x + x2 = 0 + -11.125

Combine like terms: 0 + -11.125 = -11.125
-13.4375x + x2 = -11.125

The x term is -13.4375x.  Take half its coefficient (-6.71875).
Square it (45.14160156) and add it to both sides.

Add '45.14160156' to each side of the equation.
-13.4375x + 45.14160156 + x2 = -11.125 + 45.14160156

Reorder the terms:
45.14160156 + -13.4375x + x2 = -11.125 + 45.14160156

Combine like terms: -11.125 + 45.14160156 = 34.01660156
45.14160156 + -13.4375x + x2 = 34.01660156

Factor a perfect square on the left side:
(x + -6.71875)(x + -6.71875) = 34.01660156

Calculate the square root of the right side: 5.832375293

Break this problem into two subproblems by setting 
(x + -6.71875) equal to 5.832375293 and -5.832375293.


Subproblem 1
x + -6.71875 = 5.832375293

Simplifying
x + -6.71875 = 5.832375293

Reorder the terms:
-6.71875 + x = 5.832375293

Solving
-6.71875 + x = 5.832375293

Solving for variable 'x'.

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

Add '6.71875' to each side of the equation.
-6.71875 + 6.71875 + x = 5.832375293 + 6.71875

Combine like terms: -6.71875 + 6.71875 = 0.00000
0.00000 + x = 5.832375293 + 6.71875
x = 5.832375293 + 6.71875

Combine like terms: 5.832375293 + 6.71875 = 12.551125293
x = 12.551125293

Simplifying
x = 12.551125293


Subproblem 2
x + -6.71875 = -5.832375293

Simplifying
x + -6.71875 = -5.832375293

Reorder the terms:
-6.71875 + x = -5.832375293

Solving
-6.71875 + x = -5.832375293

Solving for variable 'x'.

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

Add '6.71875' to each side of the equation.
-6.71875 + 6.71875 + x = -5.832375293 + 6.71875

Combine like terms: -6.71875 + 6.71875 = 0.00000
0.00000 + x = -5.832375293 + 6.71875
x = -5.832375293 + 6.71875

Combine like terms: -5.832375293 + 6.71875 = 0.886374707
x = 0.886374707

Simplifying
x = 0.886374707


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.551125293, 0.886374707}

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