8x^2+37x-25=-2

Solution for 8x^2+37x-25=-2 equation:

Simplifying
8x2 + 37x + -25 = -2

Reorder the terms:
-25 + 37x + 8x2 = -2

Solving
-25 + 37x + 8x2 = -2

Solving for variable 'x'.

Reorder the terms:
-25 + 2 + 37x + 8x2 = -2 + 2

Combine like terms: -25 + 2 = -23
-23 + 37x + 8x2 = -2 + 2

Combine like terms: -2 + 2 = 0
-23 + 37x + 8x2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
-2.875 + 4.625x + x2 = 0

Move the constant term to the right:

Add '2.875' to each side of the equation.
-2.875 + 4.625x + 2.875 + x2 = 0 + 2.875

Reorder the terms:
-2.875 + 2.875 + 4.625x + x2 = 0 + 2.875

Combine like terms: -2.875 + 2.875 = 0.000
0.000 + 4.625x + x2 = 0 + 2.875
4.625x + x2 = 0 + 2.875

Combine like terms: 0 + 2.875 = 2.875
4.625x + x2 = 2.875

The x term is 4.625x.  Take half its coefficient (2.3125).
Square it (5.34765625) and add it to both sides.

Add '5.34765625' to each side of the equation.
4.625x + 5.34765625 + x2 = 2.875 + 5.34765625

Reorder the terms:
5.34765625 + 4.625x + x2 = 2.875 + 5.34765625

Combine like terms: 2.875 + 5.34765625 = 8.22265625
5.34765625 + 4.625x + x2 = 8.22265625

Factor a perfect square on the left side:
(x + 2.3125)(x + 2.3125) = 8.22265625

Calculate the square root of the right side: 2.867517437

Break this problem into two subproblems by setting 
(x + 2.3125) equal to 2.867517437 and -2.867517437.

Subproblem 1
x + 2.3125 = 2.867517437

Simplifying
x + 2.3125 = 2.867517437

Reorder the terms:
2.3125 + x = 2.867517437

Solving
2.3125 + x = 2.867517437

Solving for variable 'x'.

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

Add '-2.3125' to each side of the equation.
2.3125 + -2.3125 + x = 2.867517437 + -2.3125

Combine like terms: 2.3125 + -2.3125 = 0.0000
0.0000 + x = 2.867517437 + -2.3125
x = 2.867517437 + -2.3125

Combine like terms: 2.867517437 + -2.3125 = 0.555017437
x = 0.555017437

Simplifying
x = 0.555017437

Subproblem 2
x + 2.3125 = -2.867517437

Simplifying
x + 2.3125 = -2.867517437

Reorder the terms:
2.3125 + x = -2.867517437

Solving
2.3125 + x = -2.867517437

Solving for variable 'x'.

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

Add '-2.3125' to each side of the equation.
2.3125 + -2.3125 + x = -2.867517437 + -2.3125

Combine like terms: 2.3125 + -2.3125 = 0.0000
0.0000 + x = -2.867517437 + -2.3125
x = -2.867517437 + -2.3125

Combine like terms: -2.867517437 + -2.3125 = -5.180017437
x = -5.180017437

Simplifying
x = -5.180017437

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.555017437, -5.180017437}