x^2-16x-294=0

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Solution for x^2-16x-294=0 equation: 


Simplifying
x2 + -16x + -294 = 0

Reorder the terms:
-294 + -16x + x2 = 0

Solving
-294 + -16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '294' to each side of the equation.
-294 + -16x + 294 + x2 = 0 + 294

Reorder the terms:
-294 + 294 + -16x + x2 = 0 + 294

Combine like terms: -294 + 294 = 0
0 + -16x + x2 = 0 + 294
-16x + x2 = 0 + 294

Combine like terms: 0 + 294 = 294
-16x + x2 = 294

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = 294 + 64

Reorder the terms:
64 + -16x + x2 = 294 + 64

Combine like terms: 294 + 64 = 358
64 + -16x + x2 = 358

Factor a perfect square on the left side:
(x + -8)(x + -8) = 358

Calculate the square root of the right side: 18.920887928

Break this problem into two subproblems by setting 
(x + -8) equal to 18.920887928 and -18.920887928.


Subproblem 1
x + -8 = 18.920887928

Simplifying
x + -8 = 18.920887928

Reorder the terms:
-8 + x = 18.920887928

Solving
-8 + x = 18.920887928

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 18.920887928 + 8

Combine like terms: -8 + 8 = 0
0 + x = 18.920887928 + 8
x = 18.920887928 + 8

Combine like terms: 18.920887928 + 8 = 26.920887928
x = 26.920887928

Simplifying
x = 26.920887928


Subproblem 2
x + -8 = -18.920887928

Simplifying
x + -8 = -18.920887928

Reorder the terms:
-8 + x = -18.920887928

Solving
-8 + x = -18.920887928

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -18.920887928 + 8

Combine like terms: -8 + 8 = 0
0 + x = -18.920887928 + 8
x = -18.920887928 + 8

Combine like terms: -18.920887928 + 8 = -10.920887928
x = -10.920887928

Simplifying
x = -10.920887928


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {26.920887928, -10.920887928}

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