4.9x^2+28.7x+4.2=0

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Solution for 4.9x^2+28.7x+4.2=0 equation: 


Simplifying
4.9x2 + 28.7x + 4.2 = 0

Reorder the terms:
4.2 + 28.7x + 4.9x2 = 0

Solving
4.2 + 28.7x + 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'.
0.8571428571 + 5.857142857x + x2 = 0

Move the constant term to the right:

Add '-0.8571428571' to each side of the equation.
0.8571428571 + 5.857142857x + -0.8571428571 + x2 = 0 + -0.8571428571

Reorder the terms:
0.8571428571 + -0.8571428571 + 5.857142857x + x2 = 0 + -0.8571428571

Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000
0.0000000000 + 5.857142857x + x2 = 0 + -0.8571428571
5.857142857x + x2 = 0 + -0.8571428571

Combine like terms: 0 + -0.8571428571 = -0.8571428571
5.857142857x + x2 = -0.8571428571

The x term is 5.857142857x.  Take half its coefficient (2.928571429).
Square it (8.576530615) and add it to both sides.

Add '8.576530615' to each side of the equation.
5.857142857x + 8.576530615 + x2 = -0.8571428571 + 8.576530615

Reorder the terms:
8.576530615 + 5.857142857x + x2 = -0.8571428571 + 8.576530615

Combine like terms: -0.8571428571 + 8.576530615 = 7.7193877579
8.576530615 + 5.857142857x + x2 = 7.7193877579

Factor a perfect square on the left side:
(x + 2.928571429)(x + 2.928571429) = 7.7193877579

Calculate the square root of the right side: 2.77837862

Break this problem into two subproblems by setting 
(x + 2.928571429) equal to 2.77837862 and -2.77837862.


Subproblem 1
x + 2.928571429 = 2.77837862

Simplifying
x + 2.928571429 = 2.77837862

Reorder the terms:
2.928571429 + x = 2.77837862

Solving
2.928571429 + x = 2.77837862

Solving for variable 'x'.

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

Add '-2.928571429' to each side of the equation.
2.928571429 + -2.928571429 + x = 2.77837862 + -2.928571429

Combine like terms: 2.928571429 + -2.928571429 = 0.000000000
0.000000000 + x = 2.77837862 + -2.928571429
x = 2.77837862 + -2.928571429

Combine like terms: 2.77837862 + -2.928571429 = -0.150192809
x = -0.150192809

Simplifying
x = -0.150192809


Subproblem 2
x + 2.928571429 = -2.77837862

Simplifying
x + 2.928571429 = -2.77837862

Reorder the terms:
2.928571429 + x = -2.77837862

Solving
2.928571429 + x = -2.77837862

Solving for variable 'x'.

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

Add '-2.928571429' to each side of the equation.
2.928571429 + -2.928571429 + x = -2.77837862 + -2.928571429

Combine like terms: 2.928571429 + -2.928571429 = 0.000000000
0.000000000 + x = -2.77837862 + -2.928571429
x = -2.77837862 + -2.928571429

Combine like terms: -2.77837862 + -2.928571429 = -5.706950049
x = -5.706950049

Simplifying
x = -5.706950049


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.150192809, -5.706950049}

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