x^2+37x-296=0

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Solution for x^2+37x-296=0 equation: 


Simplifying
x2 + 37x + -296 = 0

Reorder the terms:
-296 + 37x + x2 = 0

Solving
-296 + 37x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '296' to each side of the equation.
-296 + 37x + 296 + x2 = 0 + 296

Reorder the terms:
-296 + 296 + 37x + x2 = 0 + 296

Combine like terms: -296 + 296 = 0
0 + 37x + x2 = 0 + 296
37x + x2 = 0 + 296

Combine like terms: 0 + 296 = 296
37x + x2 = 296

The x term is 37x.  Take half its coefficient (18.5).
Square it (342.25) and add it to both sides.

Add '342.25' to each side of the equation.
37x + 342.25 + x2 = 296 + 342.25

Reorder the terms:
342.25 + 37x + x2 = 296 + 342.25

Combine like terms: 296 + 342.25 = 638.25
342.25 + 37x + x2 = 638.25

Factor a perfect square on the left side:
(x + 18.5)(x + 18.5) = 638.25

Calculate the square root of the right side: 25.263610193

Break this problem into two subproblems by setting 
(x + 18.5) equal to 25.263610193 and -25.263610193.


Subproblem 1
x + 18.5 = 25.263610193

Simplifying
x + 18.5 = 25.263610193

Reorder the terms:
18.5 + x = 25.263610193

Solving
18.5 + x = 25.263610193

Solving for variable 'x'.

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

Add '-18.5' to each side of the equation.
18.5 + -18.5 + x = 25.263610193 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + x = 25.263610193 + -18.5
x = 25.263610193 + -18.5

Combine like terms: 25.263610193 + -18.5 = 6.763610193
x = 6.763610193

Simplifying
x = 6.763610193


Subproblem 2
x + 18.5 = -25.263610193

Simplifying
x + 18.5 = -25.263610193

Reorder the terms:
18.5 + x = -25.263610193

Solving
18.5 + x = -25.263610193

Solving for variable 'x'.

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

Add '-18.5' to each side of the equation.
18.5 + -18.5 + x = -25.263610193 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + x = -25.263610193 + -18.5
x = -25.263610193 + -18.5

Combine like terms: -25.263610193 + -18.5 = -43.763610193
x = -43.763610193

Simplifying
x = -43.763610193


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.763610193, -43.763610193}

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