4x^2+25x+4=0

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Solution for 4x^2+25x+4=0 equation: 


Simplifying
4x2 + 25x + 4 = 0

Reorder the terms:
4 + 25x + 4x2 = 0

Solving
4 + 25x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
1 + 6.25x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 6.25x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 6.25x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6.25x + x2 = 0 + -1
6.25x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
6.25x + x2 = -1

The x term is 6.25x.  Take half its coefficient (3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
6.25x + 9.765625 + x2 = -1 + 9.765625

Reorder the terms:
9.765625 + 6.25x + x2 = -1 + 9.765625

Combine like terms: -1 + 9.765625 = 8.765625
9.765625 + 6.25x + x2 = 8.765625

Factor a perfect square on the left side:
(x + 3.125)(x + 3.125) = 8.765625

Calculate the square root of the right side: 2.960679821

Break this problem into two subproblems by setting 
(x + 3.125) equal to 2.960679821 and -2.960679821.


Subproblem 1
x + 3.125 = 2.960679821

Simplifying
x + 3.125 = 2.960679821

Reorder the terms:
3.125 + x = 2.960679821

Solving
3.125 + x = 2.960679821

Solving for variable 'x'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + x = 2.960679821 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + x = 2.960679821 + -3.125
x = 2.960679821 + -3.125

Combine like terms: 2.960679821 + -3.125 = -0.164320179
x = -0.164320179

Simplifying
x = -0.164320179


Subproblem 2
x + 3.125 = -2.960679821

Simplifying
x + 3.125 = -2.960679821

Reorder the terms:
3.125 + x = -2.960679821

Solving
3.125 + x = -2.960679821

Solving for variable 'x'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + x = -2.960679821 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + x = -2.960679821 + -3.125
x = -2.960679821 + -3.125

Combine like terms: -2.960679821 + -3.125 = -6.085679821
x = -6.085679821

Simplifying
x = -6.085679821


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.164320179, -6.085679821}

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