.25x^2+70x+49=0

Solution for .25x^2+70x+49=0 equation:

Simplifying
0.25x2 + 70x + 49 = 0

Reorder the terms:
49 + 70x + 0.25x2 = 0

Solving
49 + 70x + 0.25x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.25'.
196 + 280x + x2 = 0

Move the constant term to the right:

Add '-196' to each side of the equation.
196 + 280x + -196 + x2 = 0 + -196

Reorder the terms:
196 + -196 + 280x + x2 = 0 + -196

Combine like terms: 196 + -196 = 0
0 + 280x + x2 = 0 + -196
280x + x2 = 0 + -196

Combine like terms: 0 + -196 = -196
280x + x2 = -196

The x term is 280x.  Take half its coefficient (140).
Square it (19600) and add it to both sides.

Add '19600' to each side of the equation.
280x + 19600 + x2 = -196 + 19600

Reorder the terms:
19600 + 280x + x2 = -196 + 19600

Combine like terms: -196 + 19600 = 19404
19600 + 280x + x2 = 19404

Factor a perfect square on the left side:
(x + 140)(x + 140) = 19404

Calculate the square root of the right side: 139.298241195

Break this problem into two subproblems by setting 
(x + 140) equal to 139.298241195 and -139.298241195.

Subproblem 1
x + 140 = 139.298241195

Simplifying
x + 140 = 139.298241195

Reorder the terms:
140 + x = 139.298241195

Solving
140 + x = 139.298241195

Solving for variable 'x'.

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

Add '-140' to each side of the equation.
140 + -140 + x = 139.298241195 + -140

Combine like terms: 140 + -140 = 0
0 + x = 139.298241195 + -140
x = 139.298241195 + -140

Combine like terms: 139.298241195 + -140 = -0.701758805
x = -0.701758805

Simplifying
x = -0.701758805

Subproblem 2
x + 140 = -139.298241195

Simplifying
x + 140 = -139.298241195

Reorder the terms:
140 + x = -139.298241195

Solving
140 + x = -139.298241195

Solving for variable 'x'.

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

Add '-140' to each side of the equation.
140 + -140 + x = -139.298241195 + -140

Combine like terms: 140 + -140 = 0
0 + x = -139.298241195 + -140
x = -139.298241195 + -140

Combine like terms: -139.298241195 + -140 = -279.298241195
x = -279.298241195

Simplifying
x = -279.298241195

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.701758805, -279.298241195}