x^2-34x-24=0

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Solution for x^2-34x-24=0 equation: 


Simplifying
x2 + -34x + -24 = 0

Reorder the terms:
-24 + -34x + x2 = 0

Solving
-24 + -34x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -34x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + -34x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -34x + x2 = 0 + 24
-34x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
-34x + x2 = 24

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 = 24 + 289

Reorder the terms:
289 + -34x + x2 = 24 + 289

Combine like terms: 24 + 289 = 313
289 + -34x + x2 = 313

Factor a perfect square on the left side:
(x + -17)(x + -17) = 313

Calculate the square root of the right side: 17.691806013

Break this problem into two subproblems by setting 
(x + -17) equal to 17.691806013 and -17.691806013.


Subproblem 1
x + -17 = 17.691806013

Simplifying
x + -17 = 17.691806013

Reorder the terms:
-17 + x = 17.691806013

Solving
-17 + x = 17.691806013

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 = 17.691806013 + 17

Combine like terms: -17 + 17 = 0
0 + x = 17.691806013 + 17
x = 17.691806013 + 17

Combine like terms: 17.691806013 + 17 = 34.691806013
x = 34.691806013

Simplifying
x = 34.691806013


Subproblem 2
x + -17 = -17.691806013

Simplifying
x + -17 = -17.691806013

Reorder the terms:
-17 + x = -17.691806013

Solving
-17 + x = -17.691806013

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 = -17.691806013 + 17

Combine like terms: -17 + 17 = 0
0 + x = -17.691806013 + 17
x = -17.691806013 + 17

Combine like terms: -17.691806013 + 17 = -0.691806013
x = -0.691806013

Simplifying
x = -0.691806013


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {34.691806013, -0.691806013}

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