x^2+35x-304=0

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Solution for x^2+35x-304=0 equation: 


Simplifying
x2 + 35x + -304 = 0

Reorder the terms:
-304 + 35x + x2 = 0

Solving
-304 + 35x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '304' to each side of the equation.
-304 + 35x + 304 + x2 = 0 + 304

Reorder the terms:
-304 + 304 + 35x + x2 = 0 + 304

Combine like terms: -304 + 304 = 0
0 + 35x + x2 = 0 + 304
35x + x2 = 0 + 304

Combine like terms: 0 + 304 = 304
35x + x2 = 304

The x term is 35x.  Take half its coefficient (17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
35x + 306.25 + x2 = 304 + 306.25

Reorder the terms:
306.25 + 35x + x2 = 304 + 306.25

Combine like terms: 304 + 306.25 = 610.25
306.25 + 35x + x2 = 610.25

Factor a perfect square on the left side:
(x + 17.5)(x + 17.5) = 610.25

Calculate the square root of the right side: 24.703238654

Break this problem into two subproblems by setting 
(x + 17.5) equal to 24.703238654 and -24.703238654.


Subproblem 1
x + 17.5 = 24.703238654

Simplifying
x + 17.5 = 24.703238654

Reorder the terms:
17.5 + x = 24.703238654

Solving
17.5 + x = 24.703238654

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = 24.703238654 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = 24.703238654 + -17.5
x = 24.703238654 + -17.5

Combine like terms: 24.703238654 + -17.5 = 7.203238654
x = 7.203238654

Simplifying
x = 7.203238654


Subproblem 2
x + 17.5 = -24.703238654

Simplifying
x + 17.5 = -24.703238654

Reorder the terms:
17.5 + x = -24.703238654

Solving
17.5 + x = -24.703238654

Solving for variable 'x'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + x = -24.703238654 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + x = -24.703238654 + -17.5
x = -24.703238654 + -17.5

Combine like terms: -24.703238654 + -17.5 = -42.203238654
x = -42.203238654

Simplifying
x = -42.203238654


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.203238654, -42.203238654}

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