4.9x^2+35x+25=0

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Solution for 4.9x^2+35x+25=0 equation: 


Simplifying
4.9x2 + 35x + 25 = 0

Reorder the terms:
25 + 35x + 4.9x2 = 0

Solving
25 + 35x + 4.9x2 = 0

Solving for variable 'x'.

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

Divide each side by '4.9'.
5.102040816 + 7.142857143x + x2 = 0

Move the constant term to the right:

Add '-5.102040816' to each side of the equation.
5.102040816 + 7.142857143x + -5.102040816 + x2 = 0 + -5.102040816

Reorder the terms:
5.102040816 + -5.102040816 + 7.142857143x + x2 = 0 + -5.102040816

Combine like terms: 5.102040816 + -5.102040816 = 0.000000000
0.000000000 + 7.142857143x + x2 = 0 + -5.102040816
7.142857143x + x2 = 0 + -5.102040816

Combine like terms: 0 + -5.102040816 = -5.102040816
7.142857143x + x2 = -5.102040816

The x term is 7.142857143x.  Take half its coefficient (3.571428572).
Square it (12.75510204) and add it to both sides.

Add '12.75510204' to each side of the equation.
7.142857143x + 12.75510204 + x2 = -5.102040816 + 12.75510204

Reorder the terms:
12.75510204 + 7.142857143x + x2 = -5.102040816 + 12.75510204

Combine like terms: -5.102040816 + 12.75510204 = 7.653061224
12.75510204 + 7.142857143x + x2 = 7.653061224

Factor a perfect square on the left side:
(x + 3.571428572)(x + 3.571428572) = 7.653061224

Calculate the square root of the right side: 2.766416676

Break this problem into two subproblems by setting 
(x + 3.571428572) equal to 2.766416676 and -2.766416676.


Subproblem 1
x + 3.571428572 = 2.766416676

Simplifying
x + 3.571428572 = 2.766416676

Reorder the terms:
3.571428572 + x = 2.766416676

Solving
3.571428572 + x = 2.766416676

Solving for variable 'x'.

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

Add '-3.571428572' to each side of the equation.
3.571428572 + -3.571428572 + x = 2.766416676 + -3.571428572

Combine like terms: 3.571428572 + -3.571428572 = 0.000000000
0.000000000 + x = 2.766416676 + -3.571428572
x = 2.766416676 + -3.571428572

Combine like terms: 2.766416676 + -3.571428572 = -0.805011896
x = -0.805011896

Simplifying
x = -0.805011896


Subproblem 2
x + 3.571428572 = -2.766416676

Simplifying
x + 3.571428572 = -2.766416676

Reorder the terms:
3.571428572 + x = -2.766416676

Solving
3.571428572 + x = -2.766416676

Solving for variable 'x'.

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

Add '-3.571428572' to each side of the equation.
3.571428572 + -3.571428572 + x = -2.766416676 + -3.571428572

Combine like terms: 3.571428572 + -3.571428572 = 0.000000000
0.000000000 + x = -2.766416676 + -3.571428572
x = -2.766416676 + -3.571428572

Combine like terms: -2.766416676 + -3.571428572 = -6.337845248
x = -6.337845248

Simplifying
x = -6.337845248


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.805011896, -6.337845248}

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