25x^2+71x+49=0

Solution for 25x^2+71x+49=0 equation:

Simplifying
25x2 + 71x + 49 = 0

Reorder the terms:
49 + 71x + 25x2 = 0

Solving
49 + 71x + 25x2 = 0

Solving for variable 'x'.

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

Divide each side by '25'.
1.96 + 2.84x + x2 = 0

Move the constant term to the right:

Add '-1.96' to each side of the equation.
1.96 + 2.84x + -1.96 + x2 = 0 + -1.96

Reorder the terms:
1.96 + -1.96 + 2.84x + x2 = 0 + -1.96

Combine like terms: 1.96 + -1.96 = 0.00
0.00 + 2.84x + x2 = 0 + -1.96
2.84x + x2 = 0 + -1.96

Combine like terms: 0 + -1.96 = -1.96
2.84x + x2 = -1.96

The x term is 2.84x.  Take half its coefficient (1.42).
Square it (2.0164) and add it to both sides.

Add '2.0164' to each side of the equation.
2.84x + 2.0164 + x2 = -1.96 + 2.0164

Reorder the terms:
2.0164 + 2.84x + x2 = -1.96 + 2.0164

Combine like terms: -1.96 + 2.0164 = 0.0564
2.0164 + 2.84x + x2 = 0.0564

Factor a perfect square on the left side:
(x + 1.42)(x + 1.42) = 0.0564

Calculate the square root of the right side: 0.237486842

Break this problem into two subproblems by setting 
(x + 1.42) equal to 0.237486842 and -0.237486842.

Subproblem 1
x + 1.42 = 0.237486842

Simplifying
x + 1.42 = 0.237486842

Reorder the terms:
1.42 + x = 0.237486842

Solving
1.42 + x = 0.237486842

Solving for variable 'x'.

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

Add '-1.42' to each side of the equation.
1.42 + -1.42 + x = 0.237486842 + -1.42

Combine like terms: 1.42 + -1.42 = 0.00
0.00 + x = 0.237486842 + -1.42
x = 0.237486842 + -1.42

Combine like terms: 0.237486842 + -1.42 = -1.182513158
x = -1.182513158

Simplifying
x = -1.182513158

Subproblem 2
x + 1.42 = -0.237486842

Simplifying
x + 1.42 = -0.237486842

Reorder the terms:
1.42 + x = -0.237486842

Solving
1.42 + x = -0.237486842

Solving for variable 'x'.

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

Add '-1.42' to each side of the equation.
1.42 + -1.42 + x = -0.237486842 + -1.42

Combine like terms: 1.42 + -1.42 = 0.00
0.00 + x = -0.237486842 + -1.42
x = -0.237486842 + -1.42

Combine like terms: -0.237486842 + -1.42 = -1.657486842
x = -1.657486842

Simplifying
x = -1.657486842

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.182513158, -1.657486842}