4.9x^2+28x+2.5=0

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Solution for 4.9x^2+28x+2.5=0 equation: 


Simplifying
4.9x2 + 28x + 2.5 = 0

Reorder the terms:
2.5 + 28x + 4.9x2 = 0

Solving
2.5 + 28x + 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'.
0.5102040816 + 5.714285714x + x2 = 0

Move the constant term to the right:

Add '-0.5102040816' to each side of the equation.
0.5102040816 + 5.714285714x + -0.5102040816 + x2 = 0 + -0.5102040816

Reorder the terms:
0.5102040816 + -0.5102040816 + 5.714285714x + x2 = 0 + -0.5102040816

Combine like terms: 0.5102040816 + -0.5102040816 = 0.0000000000
0.0000000000 + 5.714285714x + x2 = 0 + -0.5102040816
5.714285714x + x2 = 0 + -0.5102040816

Combine like terms: 0 + -0.5102040816 = -0.5102040816
5.714285714x + x2 = -0.5102040816

The x term is 5.714285714x.  Take half its coefficient (2.857142857).
Square it (8.163265305) and add it to both sides.

Add '8.163265305' to each side of the equation.
5.714285714x + 8.163265305 + x2 = -0.5102040816 + 8.163265305

Reorder the terms:
8.163265305 + 5.714285714x + x2 = -0.5102040816 + 8.163265305

Combine like terms: -0.5102040816 + 8.163265305 = 7.6530612234
8.163265305 + 5.714285714x + x2 = 7.6530612234

Factor a perfect square on the left side:
(x + 2.857142857)(x + 2.857142857) = 7.6530612234

Calculate the square root of the right side: 2.766416676

Break this problem into two subproblems by setting 
(x + 2.857142857) equal to 2.766416676 and -2.766416676.


Subproblem 1
x + 2.857142857 = 2.766416676

Simplifying
x + 2.857142857 = 2.766416676

Reorder the terms:
2.857142857 + x = 2.766416676

Solving
2.857142857 + x = 2.766416676

Solving for variable 'x'.

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

Add '-2.857142857' to each side of the equation.
2.857142857 + -2.857142857 + x = 2.766416676 + -2.857142857

Combine like terms: 2.857142857 + -2.857142857 = 0.000000000
0.000000000 + x = 2.766416676 + -2.857142857
x = 2.766416676 + -2.857142857

Combine like terms: 2.766416676 + -2.857142857 = -0.090726181
x = -0.090726181

Simplifying
x = -0.090726181


Subproblem 2
x + 2.857142857 = -2.766416676

Simplifying
x + 2.857142857 = -2.766416676

Reorder the terms:
2.857142857 + x = -2.766416676

Solving
2.857142857 + x = -2.766416676

Solving for variable 'x'.

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

Add '-2.857142857' to each side of the equation.
2.857142857 + -2.857142857 + x = -2.766416676 + -2.857142857

Combine like terms: 2.857142857 + -2.857142857 = 0.000000000
0.000000000 + x = -2.766416676 + -2.857142857
x = -2.766416676 + -2.857142857

Combine like terms: -2.766416676 + -2.857142857 = -5.623559533
x = -5.623559533

Simplifying
x = -5.623559533


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.090726181, -5.623559533}

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