-0.61x^2+3.83x+1.92=0

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Solution for -0.61x^2+3.83x+1.92=0 equation:


Simplifying
-0.61x2 + 3.83x + 1.92 = 0

Reorder the terms:
1.92 + 3.83x + -0.61x2 = 0

Solving
1.92 + 3.83x + -0.61x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.61 the coefficient of the squared term: 

Divide each side by '-0.61'.
-3.147540984 + -6.278688525x + x2 = 0

Move the constant term to the right:

Add '3.147540984' to each side of the equation.
-3.147540984 + -6.278688525x + 3.147540984 + x2 = 0 + 3.147540984

Reorder the terms:
-3.147540984 + 3.147540984 + -6.278688525x + x2 = 0 + 3.147540984

Combine like terms: -3.147540984 + 3.147540984 = 0.000000000
0.000000000 + -6.278688525x + x2 = 0 + 3.147540984
-6.278688525x + x2 = 0 + 3.147540984

Combine like terms: 0 + 3.147540984 = 3.147540984
-6.278688525x + x2 = 3.147540984

The x term is -6.278688525x.  Take half its coefficient (-3.139344263).
Square it (9.855482402) and add it to both sides.

Add '9.855482402' to each side of the equation.
-6.278688525x + 9.855482402 + x2 = 3.147540984 + 9.855482402

Reorder the terms:
9.855482402 + -6.278688525x + x2 = 3.147540984 + 9.855482402

Combine like terms: 3.147540984 + 9.855482402 = 13.003023386
9.855482402 + -6.278688525x + x2 = 13.003023386

Factor a perfect square on the left side:
(x + -3.139344263)(x + -3.139344263) = 13.003023386

Calculate the square root of the right side: 3.605970519

Break this problem into two subproblems by setting 
(x + -3.139344263) equal to 3.605970519 and -3.605970519.


Subproblem 1
x + -3.139344263 = 3.605970519

Simplifying
x + -3.139344263 = 3.605970519

Reorder the terms:
-3.139344263 + x = 3.605970519

Solving
-3.139344263 + x = 3.605970519

Solving for variable 'x'.

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

Add '3.139344263' to each side of the equation.
-3.139344263 + 3.139344263 + x = 3.605970519 + 3.139344263

Combine like terms: -3.139344263 + 3.139344263 = 0.000000000
0.000000000 + x = 3.605970519 + 3.139344263
x = 3.605970519 + 3.139344263

Combine like terms: 3.605970519 + 3.139344263 = 6.745314782
x = 6.745314782

Simplifying
x = 6.745314782


Subproblem 2
x + -3.139344263 = -3.605970519

Simplifying
x + -3.139344263 = -3.605970519

Reorder the terms:
-3.139344263 + x = -3.605970519

Solving
-3.139344263 + x = -3.605970519

Solving for variable 'x'.

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

Add '3.139344263' to each side of the equation.
-3.139344263 + 3.139344263 + x = -3.605970519 + 3.139344263

Combine like terms: -3.139344263 + 3.139344263 = 0.000000000
0.000000000 + x = -3.605970519 + 3.139344263
x = -3.605970519 + 3.139344263

Combine like terms: -3.605970519 + 3.139344263 = -0.466626256
x = -0.466626256

Simplifying
x = -0.466626256


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.745314782, -0.466626256}

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