7x^2+68x+25=0

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Solution for 7x^2+68x+25=0 equation: 


Simplifying
7x2 + 68x + 25 = 0

Reorder the terms:
25 + 68x + 7x2 = 0

Solving
25 + 68x + 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 + 9.714285714x + x2 = 0

Move the constant term to the right:

Add '-3.571428571' to each side of the equation.
3.571428571 + 9.714285714x + -3.571428571 + x2 = 0 + -3.571428571

Reorder the terms:
3.571428571 + -3.571428571 + 9.714285714x + x2 = 0 + -3.571428571

Combine like terms: 3.571428571 + -3.571428571 = 0.000000000
0.000000000 + 9.714285714x + x2 = 0 + -3.571428571
9.714285714x + x2 = 0 + -3.571428571

Combine like terms: 0 + -3.571428571 = -3.571428571
9.714285714x + x2 = -3.571428571

The x term is 9.714285714x.  Take half its coefficient (4.857142857).
Square it (23.59183673) and add it to both sides.

Add '23.59183673' to each side of the equation.
9.714285714x + 23.59183673 + x2 = -3.571428571 + 23.59183673

Reorder the terms:
23.59183673 + 9.714285714x + x2 = -3.571428571 + 23.59183673

Combine like terms: -3.571428571 + 23.59183673 = 20.020408159
23.59183673 + 9.714285714x + x2 = 20.020408159

Factor a perfect square on the left side:
(x + 4.857142857)(x + 4.857142857) = 20.020408159

Calculate the square root of the right side: 4.474417075

Break this problem into two subproblems by setting 
(x + 4.857142857) equal to 4.474417075 and -4.474417075.


Subproblem 1
x + 4.857142857 = 4.474417075

Simplifying
x + 4.857142857 = 4.474417075

Reorder the terms:
4.857142857 + x = 4.474417075

Solving
4.857142857 + x = 4.474417075

Solving for variable 'x'.

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

Add '-4.857142857' to each side of the equation.
4.857142857 + -4.857142857 + x = 4.474417075 + -4.857142857

Combine like terms: 4.857142857 + -4.857142857 = 0.000000000
0.000000000 + x = 4.474417075 + -4.857142857
x = 4.474417075 + -4.857142857

Combine like terms: 4.474417075 + -4.857142857 = -0.382725782
x = -0.382725782

Simplifying
x = -0.382725782


Subproblem 2
x + 4.857142857 = -4.474417075

Simplifying
x + 4.857142857 = -4.474417075

Reorder the terms:
4.857142857 + x = -4.474417075

Solving
4.857142857 + x = -4.474417075

Solving for variable 'x'.

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

Add '-4.857142857' to each side of the equation.
4.857142857 + -4.857142857 + x = -4.474417075 + -4.857142857

Combine like terms: 4.857142857 + -4.857142857 = 0.000000000
0.000000000 + x = -4.474417075 + -4.857142857
x = -4.474417075 + -4.857142857

Combine like terms: -4.474417075 + -4.857142857 = -9.331559932
x = -9.331559932

Simplifying
x = -9.331559932


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.382725782, -9.331559932}

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