4.9*x^2+3.85*x+-0.07=0

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Solution for 4.9*x^2+3.85*x+-0.07=0 equation: 


Simplifying
4.9x2 + 3.85x + -0.07 = 0

Reorder the terms:
-0.07 + 3.85x + 4.9x2 = 0

Solving
-0.07 + 3.85x + 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'.
-0.01428571429 + 0.7857142857x + x2 = 0

Move the constant term to the right:

Add '0.01428571429' to each side of the equation.
-0.01428571429 + 0.7857142857x + 0.01428571429 + x2 = 0 + 0.01428571429

Reorder the terms:
-0.01428571429 + 0.01428571429 + 0.7857142857x + x2 = 0 + 0.01428571429

Combine like terms: -0.01428571429 + 0.01428571429 = 0.00000000000
0.00000000000 + 0.7857142857x + x2 = 0 + 0.01428571429
0.7857142857x + x2 = 0 + 0.01428571429

Combine like terms: 0 + 0.01428571429 = 0.01428571429
0.7857142857x + x2 = 0.01428571429

The x term is 0.7857142857x.  Take half its coefficient (0.3928571429).
Square it (0.1543367347) and add it to both sides.

Add '0.1543367347' to each side of the equation.
0.7857142857x + 0.1543367347 + x2 = 0.01428571429 + 0.1543367347

Reorder the terms:
0.1543367347 + 0.7857142857x + x2 = 0.01428571429 + 0.1543367347

Combine like terms: 0.01428571429 + 0.1543367347 = 0.16862244899
0.1543367347 + 0.7857142857x + x2 = 0.16862244899

Factor a perfect square on the left side:
(x + 0.3928571429)(x + 0.3928571429) = 0.16862244899

Calculate the square root of the right side: 0.410636639

Break this problem into two subproblems by setting 
(x + 0.3928571429) equal to 0.410636639 and -0.410636639.


Subproblem 1
x + 0.3928571429 = 0.410636639

Simplifying
x + 0.3928571429 = 0.410636639

Reorder the terms:
0.3928571429 + x = 0.410636639

Solving
0.3928571429 + x = 0.410636639

Solving for variable 'x'.

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

Add '-0.3928571429' to each side of the equation.
0.3928571429 + -0.3928571429 + x = 0.410636639 + -0.3928571429

Combine like terms: 0.3928571429 + -0.3928571429 = 0.0000000000
0.0000000000 + x = 0.410636639 + -0.3928571429
x = 0.410636639 + -0.3928571429

Combine like terms: 0.410636639 + -0.3928571429 = 0.0177794961
x = 0.0177794961

Simplifying
x = 0.0177794961


Subproblem 2
x + 0.3928571429 = -0.410636639

Simplifying
x + 0.3928571429 = -0.410636639

Reorder the terms:
0.3928571429 + x = -0.410636639

Solving
0.3928571429 + x = -0.410636639

Solving for variable 'x'.

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

Add '-0.3928571429' to each side of the equation.
0.3928571429 + -0.3928571429 + x = -0.410636639 + -0.3928571429

Combine like terms: 0.3928571429 + -0.3928571429 = 0.0000000000
0.0000000000 + x = -0.410636639 + -0.3928571429
x = -0.410636639 + -0.3928571429

Combine like terms: -0.410636639 + -0.3928571429 = -0.8034937819
x = -0.8034937819

Simplifying
x = -0.8034937819


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.0177794961, -0.8034937819}

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