-4.9x^2+20x-15=0

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Solution for -4.9x^2+20x-15=0 equation: 


Simplifying
-4.9x2 + 20x + -15 = 0

Reorder the terms:
-15 + 20x + -4.9x2 = 0

Solving
-15 + 20x + -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'.
3.06122449 + -4.081632653x + x2 = 0

Move the constant term to the right:

Add '-3.06122449' to each side of the equation.
3.06122449 + -4.081632653x + -3.06122449 + x2 = 0 + -3.06122449

Reorder the terms:
3.06122449 + -3.06122449 + -4.081632653x + x2 = 0 + -3.06122449

Combine like terms: 3.06122449 + -3.06122449 = 0.00000000
0.00000000 + -4.081632653x + x2 = 0 + -3.06122449
-4.081632653x + x2 = 0 + -3.06122449

Combine like terms: 0 + -3.06122449 = -3.06122449
-4.081632653x + x2 = -3.06122449

The x term is -4.081632653x.  Take half its coefficient (-2.040816327).
Square it (4.164931281) and add it to both sides.

Add '4.164931281' to each side of the equation.
-4.081632653x + 4.164931281 + x2 = -3.06122449 + 4.164931281

Reorder the terms:
4.164931281 + -4.081632653x + x2 = -3.06122449 + 4.164931281

Combine like terms: -3.06122449 + 4.164931281 = 1.103706791
4.164931281 + -4.081632653x + x2 = 1.103706791

Factor a perfect square on the left side:
(x + -2.040816327)(x + -2.040816327) = 1.103706791

Calculate the square root of the right side: 1.050574505

Break this problem into two subproblems by setting 
(x + -2.040816327) equal to 1.050574505 and -1.050574505.


Subproblem 1
x + -2.040816327 = 1.050574505

Simplifying
x + -2.040816327 = 1.050574505

Reorder the terms:
-2.040816327 + x = 1.050574505

Solving
-2.040816327 + x = 1.050574505

Solving for variable 'x'.

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

Add '2.040816327' to each side of the equation.
-2.040816327 + 2.040816327 + x = 1.050574505 + 2.040816327

Combine like terms: -2.040816327 + 2.040816327 = 0.000000000
0.000000000 + x = 1.050574505 + 2.040816327
x = 1.050574505 + 2.040816327

Combine like terms: 1.050574505 + 2.040816327 = 3.091390832
x = 3.091390832

Simplifying
x = 3.091390832


Subproblem 2
x + -2.040816327 = -1.050574505

Simplifying
x + -2.040816327 = -1.050574505

Reorder the terms:
-2.040816327 + x = -1.050574505

Solving
-2.040816327 + x = -1.050574505

Solving for variable 'x'.

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

Add '2.040816327' to each side of the equation.
-2.040816327 + 2.040816327 + x = -1.050574505 + 2.040816327

Combine like terms: -2.040816327 + 2.040816327 = 0.000000000
0.000000000 + x = -1.050574505 + 2.040816327
x = -1.050574505 + 2.040816327

Combine like terms: -1.050574505 + 2.040816327 = 0.990241822
x = 0.990241822

Simplifying
x = 0.990241822


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.091390832, 0.990241822}

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