x^2+34x-12=0

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Solution for x^2+34x-12=0 equation: 


Simplifying
x2 + 34x + -12 = 0

Reorder the terms:
-12 + 34x + x2 = 0

Solving
-12 + 34x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + 34x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + 34x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 34x + x2 = 0 + 12
34x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
34x + x2 = 12

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 = 12 + 289

Reorder the terms:
289 + 34x + x2 = 12 + 289

Combine like terms: 12 + 289 = 301
289 + 34x + x2 = 301

Factor a perfect square on the left side:
(x + 17)(x + 17) = 301

Calculate the square root of the right side: 17.349351573

Break this problem into two subproblems by setting 
(x + 17) equal to 17.349351573 and -17.349351573.


Subproblem 1
x + 17 = 17.349351573

Simplifying
x + 17 = 17.349351573

Reorder the terms:
17 + x = 17.349351573

Solving
17 + x = 17.349351573

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 = 17.349351573 + -17

Combine like terms: 17 + -17 = 0
0 + x = 17.349351573 + -17
x = 17.349351573 + -17

Combine like terms: 17.349351573 + -17 = 0.349351573
x = 0.349351573

Simplifying
x = 0.349351573


Subproblem 2
x + 17 = -17.349351573

Simplifying
x + 17 = -17.349351573

Reorder the terms:
17 + x = -17.349351573

Solving
17 + x = -17.349351573

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 = -17.349351573 + -17

Combine like terms: 17 + -17 = 0
0 + x = -17.349351573 + -17
x = -17.349351573 + -17

Combine like terms: -17.349351573 + -17 = -34.349351573
x = -34.349351573

Simplifying
x = -34.349351573


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.349351573, -34.349351573}

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