7x^2+62x+125=0

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Solution for 7x^2+62x+125=0 equation: 


Simplifying
7x2 + 62x + 125 = 0

Reorder the terms:
125 + 62x + 7x2 = 0

Solving
125 + 62x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
17.85714286 + 8.857142857x + x2 = 0

Move the constant term to the right:

Add '-17.85714286' to each side of the equation.
17.85714286 + 8.857142857x + -17.85714286 + x2 = 0 + -17.85714286

Reorder the terms:
17.85714286 + -17.85714286 + 8.857142857x + x2 = 0 + -17.85714286

Combine like terms: 17.85714286 + -17.85714286 = 0.00000000
0.00000000 + 8.857142857x + x2 = 0 + -17.85714286
8.857142857x + x2 = 0 + -17.85714286

Combine like terms: 0 + -17.85714286 = -17.85714286
8.857142857x + x2 = -17.85714286

The x term is 8.857142857x.  Take half its coefficient (4.428571429).
Square it (19.61224490) and add it to both sides.

Add '19.61224490' to each side of the equation.
8.857142857x + 19.61224490 + x2 = -17.85714286 + 19.61224490

Reorder the terms:
19.61224490 + 8.857142857x + x2 = -17.85714286 + 19.61224490

Combine like terms: -17.85714286 + 19.61224490 = 1.75510204
19.61224490 + 8.857142857x + x2 = 1.75510204

Factor a perfect square on the left side:
(x + 4.428571429)(x + 4.428571429) = 1.75510204

Calculate the square root of the right side: 1.324802642

Break this problem into two subproblems by setting 
(x + 4.428571429) equal to 1.324802642 and -1.324802642.


Subproblem 1
x + 4.428571429 = 1.324802642

Simplifying
x + 4.428571429 = 1.324802642

Reorder the terms:
4.428571429 + x = 1.324802642

Solving
4.428571429 + x = 1.324802642

Solving for variable 'x'.

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

Add '-4.428571429' to each side of the equation.
4.428571429 + -4.428571429 + x = 1.324802642 + -4.428571429

Combine like terms: 4.428571429 + -4.428571429 = 0.000000000
0.000000000 + x = 1.324802642 + -4.428571429
x = 1.324802642 + -4.428571429

Combine like terms: 1.324802642 + -4.428571429 = -3.103768787
x = -3.103768787

Simplifying
x = -3.103768787


Subproblem 2
x + 4.428571429 = -1.324802642

Simplifying
x + 4.428571429 = -1.324802642

Reorder the terms:
4.428571429 + x = -1.324802642

Solving
4.428571429 + x = -1.324802642

Solving for variable 'x'.

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

Add '-4.428571429' to each side of the equation.
4.428571429 + -4.428571429 + x = -1.324802642 + -4.428571429

Combine like terms: 4.428571429 + -4.428571429 = 0.000000000
0.000000000 + x = -1.324802642 + -4.428571429
x = -1.324802642 + -4.428571429

Combine like terms: -1.324802642 + -4.428571429 = -5.753374071
x = -5.753374071

Simplifying
x = -5.753374071


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.103768787, -5.753374071}

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