.018x^2+76.27x-21.7=0

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Solution for .018x^2+76.27x-21.7=0 equation: 


Simplifying
0.018x2 + 76.27x + -21.7 = 0

Reorder the terms:
-21.7 + 76.27x + 0.018x2 = 0

Solving
-21.7 + 76.27x + 0.018x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.018'.
-1205.555556 + 4237.222222x + x2 = 0

Move the constant term to the right:

Add '1205.555556' to each side of the equation.
-1205.555556 + 4237.222222x + 1205.555556 + x2 = 0 + 1205.555556

Reorder the terms:
-1205.555556 + 1205.555556 + 4237.222222x + x2 = 0 + 1205.555556

Combine like terms: -1205.555556 + 1205.555556 = 0.000000
0.000000 + 4237.222222x + x2 = 0 + 1205.555556
4237.222222x + x2 = 0 + 1205.555556

Combine like terms: 0 + 1205.555556 = 1205.555556
4237.222222x + x2 = 1205.555556

The x term is 4237.222222x.  Take half its coefficient (2118.611111).
Square it (4488513.040) and add it to both sides.

Add '4488513.040' to each side of the equation.
4237.222222x + 4488513.040 + x2 = 1205.555556 + 4488513.040

Reorder the terms:
4488513.040 + 4237.222222x + x2 = 1205.555556 + 4488513.040

Combine like terms: 1205.555556 + 4488513.040 = 4489718.595556
4488513.040 + 4237.222222x + x2 = 4489718.595556

Factor a perfect square on the left side:
(x + 2118.611111)(x + 2118.611111) = 4489718.595556

Calculate the square root of the right side: 2118.895607517

Break this problem into two subproblems by setting 
(x + 2118.611111) equal to 2118.895607517 and -2118.895607517.


Subproblem 1
x + 2118.611111 = 2118.895607517

Simplifying
x + 2118.611111 = 2118.895607517

Reorder the terms:
2118.611111 + x = 2118.895607517

Solving
2118.611111 + x = 2118.895607517

Solving for variable 'x'.

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

Add '-2118.611111' to each side of the equation.
2118.611111 + -2118.611111 + x = 2118.895607517 + -2118.611111

Combine like terms: 2118.611111 + -2118.611111 = 0.000000
0.000000 + x = 2118.895607517 + -2118.611111
x = 2118.895607517 + -2118.611111

Combine like terms: 2118.895607517 + -2118.611111 = 0.284496517
x = 0.284496517

Simplifying
x = 0.284496517


Subproblem 2
x + 2118.611111 = -2118.895607517

Simplifying
x + 2118.611111 = -2118.895607517

Reorder the terms:
2118.611111 + x = -2118.895607517

Solving
2118.611111 + x = -2118.895607517

Solving for variable 'x'.

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

Add '-2118.611111' to each side of the equation.
2118.611111 + -2118.611111 + x = -2118.895607517 + -2118.611111

Combine like terms: 2118.611111 + -2118.611111 = 0.000000
0.000000 + x = -2118.895607517 + -2118.611111
x = -2118.895607517 + -2118.611111

Combine like terms: -2118.895607517 + -2118.611111 = -4237.506718517
x = -4237.506718517

Simplifying
x = -4237.506718517


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.284496517, -4237.506718517}

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