20x^2+49x+25=5

Solution for 20x^2+49x+25=5 equation:

Simplifying
20x2 + 49x + 25 = 5

Reorder the terms:
25 + 49x + 20x2 = 5

Solving
25 + 49x + 20x2 = 5

Solving for variable 'x'.

Reorder the terms:
25 + -5 + 49x + 20x2 = 5 + -5

Combine like terms: 25 + -5 = 20
20 + 49x + 20x2 = 5 + -5

Combine like terms: 5 + -5 = 0
20 + 49x + 20x2 = 0

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

Divide each side by '20'.
1 + 2.45x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 2.45x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 2.45x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2.45x + x2 = 0 + -1
2.45x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
2.45x + x2 = -1

The x term is 2.45x.  Take half its coefficient (1.225).
Square it (1.500625) and add it to both sides.

Add '1.500625' to each side of the equation.
2.45x + 1.500625 + x2 = -1 + 1.500625

Reorder the terms:
1.500625 + 2.45x + x2 = -1 + 1.500625

Combine like terms: -1 + 1.500625 = 0.500625
1.500625 + 2.45x + x2 = 0.500625

Factor a perfect square on the left side:
(x + 1.225)(x + 1.225) = 0.500625

Calculate the square root of the right side: 0.707548585

Break this problem into two subproblems by setting 
(x + 1.225) equal to 0.707548585 and -0.707548585.

Subproblem 1
x + 1.225 = 0.707548585

Simplifying
x + 1.225 = 0.707548585

Reorder the terms:
1.225 + x = 0.707548585

Solving
1.225 + x = 0.707548585

Solving for variable 'x'.

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

Add '-1.225' to each side of the equation.
1.225 + -1.225 + x = 0.707548585 + -1.225

Combine like terms: 1.225 + -1.225 = 0.000
0.000 + x = 0.707548585 + -1.225
x = 0.707548585 + -1.225

Combine like terms: 0.707548585 + -1.225 = -0.517451415
x = -0.517451415

Simplifying
x = -0.517451415

Subproblem 2
x + 1.225 = -0.707548585

Simplifying
x + 1.225 = -0.707548585

Reorder the terms:
1.225 + x = -0.707548585

Solving
1.225 + x = -0.707548585

Solving for variable 'x'.

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

Add '-1.225' to each side of the equation.
1.225 + -1.225 + x = -0.707548585 + -1.225

Combine like terms: 1.225 + -1.225 = 0.000
0.000 + x = -0.707548585 + -1.225
x = -0.707548585 + -1.225

Combine like terms: -0.707548585 + -1.225 = -1.932548585
x = -1.932548585

Simplifying
x = -1.932548585

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.517451415, -1.932548585}