x^2-34x-25=0

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Solution for x^2-34x-25=0 equation: 


Simplifying
x2 + -34x + -25 = 0

Reorder the terms:
-25 + -34x + x2 = 0

Solving
-25 + -34x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -34x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + -34x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -34x + x2 = 0 + 25
-34x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
-34x + x2 = 25

The x term is -34x.  Take half its coefficient (-17).
Square it (289) and add it to both sides.

Add '289' to each side of the equation.
-34x + 289 + x2 = 25 + 289

Reorder the terms:
289 + -34x + x2 = 25 + 289

Combine like terms: 25 + 289 = 314
289 + -34x + x2 = 314

Factor a perfect square on the left side:
(x + -17)(x + -17) = 314

Calculate the square root of the right side: 17.720045147

Break this problem into two subproblems by setting 
(x + -17) equal to 17.720045147 and -17.720045147.


Subproblem 1
x + -17 = 17.720045147

Simplifying
x + -17 = 17.720045147

Reorder the terms:
-17 + x = 17.720045147

Solving
-17 + x = 17.720045147

Solving for variable 'x'.

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

Add '17' to each side of the equation.
-17 + 17 + x = 17.720045147 + 17

Combine like terms: -17 + 17 = 0
0 + x = 17.720045147 + 17
x = 17.720045147 + 17

Combine like terms: 17.720045147 + 17 = 34.720045147
x = 34.720045147

Simplifying
x = 34.720045147


Subproblem 2
x + -17 = -17.720045147

Simplifying
x + -17 = -17.720045147

Reorder the terms:
-17 + x = -17.720045147

Solving
-17 + x = -17.720045147

Solving for variable 'x'.

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

Add '17' to each side of the equation.
-17 + 17 + x = -17.720045147 + 17

Combine like terms: -17 + 17 = 0
0 + x = -17.720045147 + 17
x = -17.720045147 + 17

Combine like terms: -17.720045147 + 17 = -0.720045147
x = -0.720045147

Simplifying
x = -0.720045147


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {34.720045147, -0.720045147}

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