4.8x^2-27.8x-28=0

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Solution for 4.8x^2-27.8x-28=0 equation: 


Simplifying
4.8x2 + -27.8x + -28 = 0

Reorder the terms:
-28 + -27.8x + 4.8x2 = 0

Solving
-28 + -27.8x + 4.8x2 = 0

Solving for variable 'x'.

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

Divide each side by '4.8'.
-5.833333333 + -5.791666667x + x2 = 0

Move the constant term to the right:

Add '5.833333333' to each side of the equation.
-5.833333333 + -5.791666667x + 5.833333333 + x2 = 0 + 5.833333333

Reorder the terms:
-5.833333333 + 5.833333333 + -5.791666667x + x2 = 0 + 5.833333333

Combine like terms: -5.833333333 + 5.833333333 = 0.000000000
0.000000000 + -5.791666667x + x2 = 0 + 5.833333333
-5.791666667x + x2 = 0 + 5.833333333

Combine like terms: 0 + 5.833333333 = 5.833333333
-5.791666667x + x2 = 5.833333333

The x term is -5.791666667x.  Take half its coefficient (-2.895833334).
Square it (8.385850698) and add it to both sides.

Add '8.385850698' to each side of the equation.
-5.791666667x + 8.385850698 + x2 = 5.833333333 + 8.385850698

Reorder the terms:
8.385850698 + -5.791666667x + x2 = 5.833333333 + 8.385850698

Combine like terms: 5.833333333 + 8.385850698 = 14.219184031
8.385850698 + -5.791666667x + x2 = 14.219184031

Factor a perfect square on the left side:
(x + -2.895833334)(x + -2.895833334) = 14.219184031

Calculate the square root of the right side: 3.770833334

Break this problem into two subproblems by setting 
(x + -2.895833334) equal to 3.770833334 and -3.770833334.


Subproblem 1
x + -2.895833334 = 3.770833334

Simplifying
x + -2.895833334 = 3.770833334

Reorder the terms:
-2.895833334 + x = 3.770833334

Solving
-2.895833334 + x = 3.770833334

Solving for variable 'x'.

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

Add '2.895833334' to each side of the equation.
-2.895833334 + 2.895833334 + x = 3.770833334 + 2.895833334

Combine like terms: -2.895833334 + 2.895833334 = 0.000000000
0.000000000 + x = 3.770833334 + 2.895833334
x = 3.770833334 + 2.895833334

Combine like terms: 3.770833334 + 2.895833334 = 6.666666668
x = 6.666666668

Simplifying
x = 6.666666668


Subproblem 2
x + -2.895833334 = -3.770833334

Simplifying
x + -2.895833334 = -3.770833334

Reorder the terms:
-2.895833334 + x = -3.770833334

Solving
-2.895833334 + x = -3.770833334

Solving for variable 'x'.

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

Add '2.895833334' to each side of the equation.
-2.895833334 + 2.895833334 + x = -3.770833334 + 2.895833334

Combine like terms: -2.895833334 + 2.895833334 = 0.000000000
0.000000000 + x = -3.770833334 + 2.895833334
x = -3.770833334 + 2.895833334

Combine like terms: -3.770833334 + 2.895833334 = -0.875
x = -0.875

Simplifying
x = -0.875


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.666666668, -0.875}

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