x^2-136x-350=0

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Solution for x^2-136x-350=0 equation: 


Simplifying
x2 + -136x + -350 = 0

Reorder the terms:
-350 + -136x + x2 = 0

Solving
-350 + -136x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '350' to each side of the equation.
-350 + -136x + 350 + x2 = 0 + 350

Reorder the terms:
-350 + 350 + -136x + x2 = 0 + 350

Combine like terms: -350 + 350 = 0
0 + -136x + x2 = 0 + 350
-136x + x2 = 0 + 350

Combine like terms: 0 + 350 = 350
-136x + x2 = 350

The x term is -136x.  Take half its coefficient (-68).
Square it (4624) and add it to both sides.

Add '4624' to each side of the equation.
-136x + 4624 + x2 = 350 + 4624

Reorder the terms:
4624 + -136x + x2 = 350 + 4624

Combine like terms: 350 + 4624 = 4974
4624 + -136x + x2 = 4974

Factor a perfect square on the left side:
(x + -68)(x + -68) = 4974

Calculate the square root of the right side: 70.52659073

Break this problem into two subproblems by setting 
(x + -68) equal to 70.52659073 and -70.52659073.


Subproblem 1
x + -68 = 70.52659073

Simplifying
x + -68 = 70.52659073

Reorder the terms:
-68 + x = 70.52659073

Solving
-68 + x = 70.52659073

Solving for variable 'x'.

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

Add '68' to each side of the equation.
-68 + 68 + x = 70.52659073 + 68

Combine like terms: -68 + 68 = 0
0 + x = 70.52659073 + 68
x = 70.52659073 + 68

Combine like terms: 70.52659073 + 68 = 138.52659073
x = 138.52659073

Simplifying
x = 138.52659073


Subproblem 2
x + -68 = -70.52659073

Simplifying
x + -68 = -70.52659073

Reorder the terms:
-68 + x = -70.52659073

Solving
-68 + x = -70.52659073

Solving for variable 'x'.

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

Add '68' to each side of the equation.
-68 + 68 + x = -70.52659073 + 68

Combine like terms: -68 + 68 = 0
0 + x = -70.52659073 + 68
x = -70.52659073 + 68

Combine like terms: -70.52659073 + 68 = -2.52659073
x = -2.52659073

Simplifying
x = -2.52659073


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {138.52659073, -2.52659073}

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