4.8x^2-x-4=0

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Solution for 4.8x^2-x-4=0 equation:


Simplifying
4.8x2 + -1x + -4 = 0

Reorder the terms:
-4 + -1x + 4.8x2 = 0

Solving
-4 + -1x + 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'.
-0.8333333333 + -0.2083333333x + x2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -0.2083333333x + 0.8333333333 + x2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -0.2083333333x + x2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -0.2083333333x + x2 = 0 + 0.8333333333
-0.2083333333x + x2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-0.2083333333x + x2 = 0.8333333333

The x term is -0.2083333333x.  Take half its coefficient (-0.1041666667).
Square it (0.01085069445) and add it to both sides.

Add '0.01085069445' to each side of the equation.
-0.2083333333x + 0.01085069445 + x2 = 0.8333333333 + 0.01085069445

Reorder the terms:
0.01085069445 + -0.2083333333x + x2 = 0.8333333333 + 0.01085069445

Combine like terms: 0.8333333333 + 0.01085069445 = 0.84418402775
0.01085069445 + -0.2083333333x + x2 = 0.84418402775

Factor a perfect square on the left side:
(x + -0.1041666667)(x + -0.1041666667) = 0.84418402775

Calculate the square root of the right side: 0.918794878

Break this problem into two subproblems by setting 
(x + -0.1041666667) equal to 0.918794878 and -0.918794878.


Subproblem 1
x + -0.1041666667 = 0.918794878

Simplifying
x + -0.1041666667 = 0.918794878

Reorder the terms:
-0.1041666667 + x = 0.918794878

Solving
-0.1041666667 + x = 0.918794878

Solving for variable 'x'.

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

Add '0.1041666667' to each side of the equation.
-0.1041666667 + 0.1041666667 + x = 0.918794878 + 0.1041666667

Combine like terms: -0.1041666667 + 0.1041666667 = 0.0000000000
0.0000000000 + x = 0.918794878 + 0.1041666667
x = 0.918794878 + 0.1041666667

Combine like terms: 0.918794878 + 0.1041666667 = 1.0229615447
x = 1.0229615447

Simplifying
x = 1.0229615447


Subproblem 2
x + -0.1041666667 = -0.918794878

Simplifying
x + -0.1041666667 = -0.918794878

Reorder the terms:
-0.1041666667 + x = -0.918794878

Solving
-0.1041666667 + x = -0.918794878

Solving for variable 'x'.

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

Add '0.1041666667' to each side of the equation.
-0.1041666667 + 0.1041666667 + x = -0.918794878 + 0.1041666667

Combine like terms: -0.1041666667 + 0.1041666667 = 0.0000000000
0.0000000000 + x = -0.918794878 + 0.1041666667
x = -0.918794878 + 0.1041666667

Combine like terms: -0.918794878 + 0.1041666667 = -0.8146282113
x = -0.8146282113

Simplifying
x = -0.8146282113


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.0229615447, -0.8146282113}

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