4.9x^2-9.19x-20=0

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Solution for 4.9x^2-9.19x-20=0 equation: 


Simplifying
4.9x2 + -9.19x + -20 = 0

Reorder the terms:
-20 + -9.19x + 4.9x2 = 0

Solving
-20 + -9.19x + 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'.
-4.081632653 + -1.875510204x + x2 = 0

Move the constant term to the right:

Add '4.081632653' to each side of the equation.
-4.081632653 + -1.875510204x + 4.081632653 + x2 = 0 + 4.081632653

Reorder the terms:
-4.081632653 + 4.081632653 + -1.875510204x + x2 = 0 + 4.081632653

Combine like terms: -4.081632653 + 4.081632653 = 0.000000000
0.000000000 + -1.875510204x + x2 = 0 + 4.081632653
-1.875510204x + x2 = 0 + 4.081632653

Combine like terms: 0 + 4.081632653 = 4.081632653
-1.875510204x + x2 = 4.081632653

The x term is -1.875510204x.  Take half its coefficient (-0.937755102).
Square it (0.8793846313) and add it to both sides.

Add '0.8793846313' to each side of the equation.
-1.875510204x + 0.8793846313 + x2 = 4.081632653 + 0.8793846313

Reorder the terms:
0.8793846313 + -1.875510204x + x2 = 4.081632653 + 0.8793846313

Combine like terms: 4.081632653 + 0.8793846313 = 4.9610172843
0.8793846313 + -1.875510204x + x2 = 4.9610172843

Factor a perfect square on the left side:
(x + -0.937755102)(x + -0.937755102) = 4.9610172843

Calculate the square root of the right side: 2.22733412

Break this problem into two subproblems by setting 
(x + -0.937755102) equal to 2.22733412 and -2.22733412.


Subproblem 1
x + -0.937755102 = 2.22733412

Simplifying
x + -0.937755102 = 2.22733412

Reorder the terms:
-0.937755102 + x = 2.22733412

Solving
-0.937755102 + x = 2.22733412

Solving for variable 'x'.

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

Add '0.937755102' to each side of the equation.
-0.937755102 + 0.937755102 + x = 2.22733412 + 0.937755102

Combine like terms: -0.937755102 + 0.937755102 = 0.000000000
0.000000000 + x = 2.22733412 + 0.937755102
x = 2.22733412 + 0.937755102

Combine like terms: 2.22733412 + 0.937755102 = 3.165089222
x = 3.165089222

Simplifying
x = 3.165089222


Subproblem 2
x + -0.937755102 = -2.22733412

Simplifying
x + -0.937755102 = -2.22733412

Reorder the terms:
-0.937755102 + x = -2.22733412

Solving
-0.937755102 + x = -2.22733412

Solving for variable 'x'.

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

Add '0.937755102' to each side of the equation.
-0.937755102 + 0.937755102 + x = -2.22733412 + 0.937755102

Combine like terms: -0.937755102 + 0.937755102 = 0.000000000
0.000000000 + x = -2.22733412 + 0.937755102
x = -2.22733412 + 0.937755102

Combine like terms: -2.22733412 + 0.937755102 = -1.289579018
x = -1.289579018

Simplifying
x = -1.289579018


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.165089222, -1.289579018}

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