25=16x^2+35x+5

Solution for 25=16x^2+35x+5 equation:

Simplifying
25 = 16x2 + 35x + 5

Reorder the terms:
25 = 5 + 35x + 16x2

Solving
25 = 5 + 35x + 16x2

Solving for variable 'x'.

Combine like terms: 25 + -5 = 20
20 + -35x + -16x2 = 5 + 35x + 16x2 + -5 + -35x + -16x2

Reorder the terms:
20 + -35x + -16x2 = 5 + -5 + 35x + -35x + 16x2 + -16x2

Combine like terms: 5 + -5 = 0
20 + -35x + -16x2 = 0 + 35x + -35x + 16x2 + -16x2
20 + -35x + -16x2 = 35x + -35x + 16x2 + -16x2

Combine like terms: 35x + -35x = 0
20 + -35x + -16x2 = 0 + 16x2 + -16x2
20 + -35x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
20 + -35x + -16x2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-1.25 + 2.1875x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 2.1875x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 2.1875x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 2.1875x + x2 = 0 + 1.25
2.1875x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
2.1875x + x2 = 1.25

The x term is 2.1875x.  Take half its coefficient (1.09375).
Square it (1.196289063) and add it to both sides.

Add '1.196289063' to each side of the equation.
2.1875x + 1.196289063 + x2 = 1.25 + 1.196289063

Reorder the terms:
1.196289063 + 2.1875x + x2 = 1.25 + 1.196289063

Combine like terms: 1.25 + 1.196289063 = 2.446289063
1.196289063 + 2.1875x + x2 = 2.446289063

Factor a perfect square on the left side:
(x + 1.09375)(x + 1.09375) = 2.446289063

Calculate the square root of the right side: 1.56406172

Break this problem into two subproblems by setting 
(x + 1.09375) equal to 1.56406172 and -1.56406172.

Subproblem 1
x + 1.09375 = 1.56406172

Simplifying
x + 1.09375 = 1.56406172

Reorder the terms:
1.09375 + x = 1.56406172

Solving
1.09375 + x = 1.56406172

Solving for variable 'x'.

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

Add '-1.09375' to each side of the equation.
1.09375 + -1.09375 + x = 1.56406172 + -1.09375

Combine like terms: 1.09375 + -1.09375 = 0.00000
0.00000 + x = 1.56406172 + -1.09375
x = 1.56406172 + -1.09375

Combine like terms: 1.56406172 + -1.09375 = 0.47031172
x = 0.47031172

Simplifying
x = 0.47031172

Subproblem 2
x + 1.09375 = -1.56406172

Simplifying
x + 1.09375 = -1.56406172

Reorder the terms:
1.09375 + x = -1.56406172

Solving
1.09375 + x = -1.56406172

Solving for variable 'x'.

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

Add '-1.09375' to each side of the equation.
1.09375 + -1.09375 + x = -1.56406172 + -1.09375

Combine like terms: 1.09375 + -1.09375 = 0.00000
0.00000 + x = -1.56406172 + -1.09375
x = -1.56406172 + -1.09375

Combine like terms: -1.56406172 + -1.09375 = -2.65781172
x = -2.65781172

Simplifying
x = -2.65781172

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.47031172, -2.65781172}