35x^2+25x+4=0

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Solution for 35x^2+25x+4=0 equation:


Simplifying
35x2 + 25x + 4 = 0

Reorder the terms:
4 + 25x + 35x2 = 0

Solving
4 + 25x + 35x2 = 0

Solving for variable 'x'.

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

Divide each side by '35'.
0.1142857143 + 0.7142857143x + x2 = 0

Move the constant term to the right:

Add '-0.1142857143' to each side of the equation.
0.1142857143 + 0.7142857143x + -0.1142857143 + x2 = 0 + -0.1142857143

Reorder the terms:
0.1142857143 + -0.1142857143 + 0.7142857143x + x2 = 0 + -0.1142857143

Combine like terms: 0.1142857143 + -0.1142857143 = 0.0000000000
0.0000000000 + 0.7142857143x + x2 = 0 + -0.1142857143
0.7142857143x + x2 = 0 + -0.1142857143

Combine like terms: 0 + -0.1142857143 = -0.1142857143
0.7142857143x + x2 = -0.1142857143

The x term is 0.7142857143x.  Take half its coefficient (0.3571428572).
Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.
0.7142857143x + 0.1275510204 + x2 = -0.1142857143 + 0.1275510204

Reorder the terms:
0.1275510204 + 0.7142857143x + x2 = -0.1142857143 + 0.1275510204

Combine like terms: -0.1142857143 + 0.1275510204 = 0.0132653061
0.1275510204 + 0.7142857143x + x2 = 0.0132653061

Factor a perfect square on the left side:
(x + 0.3571428572)(x + 0.3571428572) = 0.0132653061

Calculate the square root of the right side: 0.115175111

Break this problem into two subproblems by setting 
(x + 0.3571428572) equal to 0.115175111 and -0.115175111.

Subproblem 1

x + 0.3571428572 = 0.115175111 Simplifying x + 0.3571428572 = 0.115175111 Reorder the terms: 0.3571428572 + x = 0.115175111 Solving 0.3571428572 + x = 0.115175111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = 0.115175111 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = 0.115175111 + -0.3571428572 x = 0.115175111 + -0.3571428572 Combine like terms: 0.115175111 + -0.3571428572 = -0.2419677462 x = -0.2419677462 Simplifying x = -0.2419677462

Subproblem 2

x + 0.3571428572 = -0.115175111 Simplifying x + 0.3571428572 = -0.115175111 Reorder the terms: 0.3571428572 + x = -0.115175111 Solving 0.3571428572 + x = -0.115175111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x = -0.115175111 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x = -0.115175111 + -0.3571428572 x = -0.115175111 + -0.3571428572 Combine like terms: -0.115175111 + -0.3571428572 = -0.4723179682 x = -0.4723179682 Simplifying x = -0.4723179682

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.2419677462, -0.4723179682}

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