x^2+34x+45=0

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Solution for x^2+34x+45=0 equation: 


Simplifying
x2 + 34x + 45 = 0

Reorder the terms:
45 + 34x + x2 = 0

Solving
45 + 34x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-45' to each side of the equation.
45 + 34x + -45 + x2 = 0 + -45

Reorder the terms:
45 + -45 + 34x + x2 = 0 + -45

Combine like terms: 45 + -45 = 0
0 + 34x + x2 = 0 + -45
34x + x2 = 0 + -45

Combine like terms: 0 + -45 = -45
34x + x2 = -45

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 = -45 + 289

Reorder the terms:
289 + 34x + x2 = -45 + 289

Combine like terms: -45 + 289 = 244
289 + 34x + x2 = 244

Factor a perfect square on the left side:
(x + 17)(x + 17) = 244

Calculate the square root of the right side: 15.620499352

Break this problem into two subproblems by setting 
(x + 17) equal to 15.620499352 and -15.620499352.


Subproblem 1
x + 17 = 15.620499352

Simplifying
x + 17 = 15.620499352

Reorder the terms:
17 + x = 15.620499352

Solving
17 + x = 15.620499352

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 = 15.620499352 + -17

Combine like terms: 17 + -17 = 0
0 + x = 15.620499352 + -17
x = 15.620499352 + -17

Combine like terms: 15.620499352 + -17 = -1.379500648
x = -1.379500648

Simplifying
x = -1.379500648


Subproblem 2
x + 17 = -15.620499352

Simplifying
x + 17 = -15.620499352

Reorder the terms:
17 + x = -15.620499352

Solving
17 + x = -15.620499352

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 = -15.620499352 + -17

Combine like terms: 17 + -17 = 0
0 + x = -15.620499352 + -17
x = -15.620499352 + -17

Combine like terms: -15.620499352 + -17 = -32.620499352
x = -32.620499352

Simplifying
x = -32.620499352


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.379500648, -32.620499352}

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