7x^2+62x+25=0

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Solution for 7x^2+62x+25=0 equation: 


Simplifying
7x2 + 62x + 25 = 0

Reorder the terms:
25 + 62x + 7x2 = 0

Solving
25 + 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'.
3.571428571 + 8.857142857x + x2 = 0

Move the constant term to the right:

Add '-3.571428571' to each side of the equation.
3.571428571 + 8.857142857x + -3.571428571 + x2 = 0 + -3.571428571

Reorder the terms:
3.571428571 + -3.571428571 + 8.857142857x + x2 = 0 + -3.571428571

Combine like terms: 3.571428571 + -3.571428571 = 0.000000000
0.000000000 + 8.857142857x + x2 = 0 + -3.571428571
8.857142857x + x2 = 0 + -3.571428571

Combine like terms: 0 + -3.571428571 = -3.571428571
8.857142857x + x2 = -3.571428571

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 = -3.571428571 + 19.61224490

Reorder the terms:
19.61224490 + 8.857142857x + x2 = -3.571428571 + 19.61224490

Combine like terms: -3.571428571 + 19.61224490 = 16.040816329
19.61224490 + 8.857142857x + x2 = 16.040816329

Factor a perfect square on the left side:
(x + 4.428571429)(x + 4.428571429) = 16.040816329

Calculate the square root of the right side: 4.005098791

Break this problem into two subproblems by setting 
(x + 4.428571429) equal to 4.005098791 and -4.005098791.


Subproblem 1
x + 4.428571429 = 4.005098791

Simplifying
x + 4.428571429 = 4.005098791

Reorder the terms:
4.428571429 + x = 4.005098791

Solving
4.428571429 + x = 4.005098791

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 = 4.005098791 + -4.428571429

Combine like terms: 4.428571429 + -4.428571429 = 0.000000000
0.000000000 + x = 4.005098791 + -4.428571429
x = 4.005098791 + -4.428571429

Combine like terms: 4.005098791 + -4.428571429 = -0.423472638
x = -0.423472638

Simplifying
x = -0.423472638


Subproblem 2
x + 4.428571429 = -4.005098791

Simplifying
x + 4.428571429 = -4.005098791

Reorder the terms:
4.428571429 + x = -4.005098791

Solving
4.428571429 + x = -4.005098791

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 = -4.005098791 + -4.428571429

Combine like terms: 4.428571429 + -4.428571429 = 0.000000000
0.000000000 + x = -4.005098791 + -4.428571429
x = -4.005098791 + -4.428571429

Combine like terms: -4.005098791 + -4.428571429 = -8.43367022
x = -8.43367022

Simplifying
x = -8.43367022


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.423472638, -8.43367022}

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