x^2+36x+17=

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Solution for x^2+36x+17= equation:


Simplifying
x2 + 36x + 17 = 0

Reorder the terms:
17 + 36x + x2 = 0

Solving
17 + 36x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + 36x + -17 + x2 = 0 + -17

Reorder the terms:
17 + -17 + 36x + x2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 36x + x2 = 0 + -17
36x + x2 = 0 + -17

Combine like terms: 0 + -17 = -17
36x + x2 = -17

The x term is 36x.  Take half its coefficient (18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
36x + 324 + x2 = -17 + 324

Reorder the terms:
324 + 36x + x2 = -17 + 324

Combine like terms: -17 + 324 = 307
324 + 36x + x2 = 307

Factor a perfect square on the left side:
(x + 18)(x + 18) = 307

Calculate the square root of the right side: 17.521415468

Break this problem into two subproblems by setting 
(x + 18) equal to 17.521415468 and -17.521415468.

Subproblem 1

x + 18 = 17.521415468 Simplifying x + 18 = 17.521415468 Reorder the terms: 18 + x = 17.521415468 Solving 18 + x = 17.521415468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 17.521415468 + -18 Combine like terms: 18 + -18 = 0 0 + x = 17.521415468 + -18 x = 17.521415468 + -18 Combine like terms: 17.521415468 + -18 = -0.478584532 x = -0.478584532 Simplifying x = -0.478584532

Subproblem 2

x + 18 = -17.521415468 Simplifying x + 18 = -17.521415468 Reorder the terms: 18 + x = -17.521415468 Solving 18 + x = -17.521415468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -17.521415468 + -18 Combine like terms: 18 + -18 = 0 0 + x = -17.521415468 + -18 x = -17.521415468 + -18 Combine like terms: -17.521415468 + -18 = -35.521415468 x = -35.521415468 Simplifying x = -35.521415468

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.478584532, -35.521415468}

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