4.9*x^2+5.5*x+-0.065=0

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Solution for 4.9*x^2+5.5*x+-0.065=0 equation: 


Simplifying
4.9x2 + 5.5x + -0.065 = 0

Reorder the terms:
-0.065 + 5.5x + 4.9x2 = 0

Solving
-0.065 + 5.5x + 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'.
-0.01326530612 + 1.12244898x + x2 = 0

Move the constant term to the right:

Add '0.01326530612' to each side of the equation.
-0.01326530612 + 1.12244898x + 0.01326530612 + x2 = 0 + 0.01326530612

Reorder the terms:
-0.01326530612 + 0.01326530612 + 1.12244898x + x2 = 0 + 0.01326530612

Combine like terms: -0.01326530612 + 0.01326530612 = 0.00000000000
0.00000000000 + 1.12244898x + x2 = 0 + 0.01326530612
1.12244898x + x2 = 0 + 0.01326530612

Combine like terms: 0 + 0.01326530612 = 0.01326530612
1.12244898x + x2 = 0.01326530612

The x term is 1.12244898x.  Take half its coefficient (0.56122449).
Square it (0.3149729282) and add it to both sides.

Add '0.3149729282' to each side of the equation.
1.12244898x + 0.3149729282 + x2 = 0.01326530612 + 0.3149729282

Reorder the terms:
0.3149729282 + 1.12244898x + x2 = 0.01326530612 + 0.3149729282

Combine like terms: 0.01326530612 + 0.3149729282 = 0.32823823432
0.3149729282 + 1.12244898x + x2 = 0.32823823432

Factor a perfect square on the left side:
(x + 0.56122449)(x + 0.56122449) = 0.32823823432

Calculate the square root of the right side: 0.572920792

Break this problem into two subproblems by setting 
(x + 0.56122449) equal to 0.572920792 and -0.572920792.


Subproblem 1
x + 0.56122449 = 0.572920792

Simplifying
x + 0.56122449 = 0.572920792

Reorder the terms:
0.56122449 + x = 0.572920792

Solving
0.56122449 + x = 0.572920792

Solving for variable 'x'.

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

Add '-0.56122449' to each side of the equation.
0.56122449 + -0.56122449 + x = 0.572920792 + -0.56122449

Combine like terms: 0.56122449 + -0.56122449 = 0.00000000
0.00000000 + x = 0.572920792 + -0.56122449
x = 0.572920792 + -0.56122449

Combine like terms: 0.572920792 + -0.56122449 = 0.011696302
x = 0.011696302

Simplifying
x = 0.011696302


Subproblem 2
x + 0.56122449 = -0.572920792

Simplifying
x + 0.56122449 = -0.572920792

Reorder the terms:
0.56122449 + x = -0.572920792

Solving
0.56122449 + x = -0.572920792

Solving for variable 'x'.

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

Add '-0.56122449' to each side of the equation.
0.56122449 + -0.56122449 + x = -0.572920792 + -0.56122449

Combine like terms: 0.56122449 + -0.56122449 = 0.00000000
0.00000000 + x = -0.572920792 + -0.56122449
x = -0.572920792 + -0.56122449

Combine like terms: -0.572920792 + -0.56122449 = -1.134145282
x = -1.134145282

Simplifying
x = -1.134145282


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.011696302, -1.134145282}

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