530=-1.703x^2+37.74x+384.491

Solution for 530=-1.703x^2+37.74x+384.491 equation:

Simplifying
530 = -1.703x2 + 37.74x + 384.491

Reorder the terms:
530 = 384.491 + 37.74x + -1.703x2

Solving
530 = 384.491 + 37.74x + -1.703x2

Solving for variable 'x'.

Combine like terms: 530 + -384.491 = 145.509
145.509 + -37.74x + 1.703x2 = 384.491 + 37.74x + -1.703x2 + -384.491 + -37.74x + 1.703x2

Reorder the terms:
145.509 + -37.74x + 1.703x2 = 384.491 + -384.491 + 37.74x + -37.74x + -1.703x2 + 1.703x2

Combine like terms: 384.491 + -384.491 = 0.000
145.509 + -37.74x + 1.703x2 = 0.000 + 37.74x + -37.74x + -1.703x2 + 1.703x2
145.509 + -37.74x + 1.703x2 = 37.74x + -37.74x + -1.703x2 + 1.703x2

Combine like terms: 37.74x + -37.74x = 0.00
145.509 + -37.74x + 1.703x2 = 0.00 + -1.703x2 + 1.703x2
145.509 + -37.74x + 1.703x2 = -1.703x2 + 1.703x2

Combine like terms: -1.703x2 + 1.703x2 = 0.000
145.509 + -37.74x + 1.703x2 = 0.000

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

Divide each side by '1.703'.
85.44274809 + -22.16089254x + x2 = 0

Move the constant term to the right:

Add '-85.44274809' to each side of the equation.
85.44274809 + -22.16089254x + -85.44274809 + x2 = 0 + -85.44274809

Reorder the terms:
85.44274809 + -85.44274809 + -22.16089254x + x2 = 0 + -85.44274809

Combine like terms: 85.44274809 + -85.44274809 = 0.00000000
0.00000000 + -22.16089254x + x2 = 0 + -85.44274809
-22.16089254x + x2 = 0 + -85.44274809

Combine like terms: 0 + -85.44274809 = -85.44274809
-22.16089254x + x2 = -85.44274809

The x term is -22.16089254x.  Take half its coefficient (-11.08044627).
Square it (122.7762895) and add it to both sides.

Add '122.7762895' to each side of the equation.
-22.16089254x + 122.7762895 + x2 = -85.44274809 + 122.7762895

Reorder the terms:
122.7762895 + -22.16089254x + x2 = -85.44274809 + 122.7762895

Combine like terms: -85.44274809 + 122.7762895 = 37.33354141
122.7762895 + -22.16089254x + x2 = 37.33354141

Factor a perfect square on the left side:
(x + -11.08044627)(x + -11.08044627) = 37.33354141

Calculate the square root of the right side: 6.110117954

Break this problem into two subproblems by setting 
(x + -11.08044627) equal to 6.110117954 and -6.110117954.

Subproblem 1
x + -11.08044627 = 6.110117954

Simplifying
x + -11.08044627 = 6.110117954

Reorder the terms:
-11.08044627 + x = 6.110117954

Solving
-11.08044627 + x = 6.110117954

Solving for variable 'x'.

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

Add '11.08044627' to each side of the equation.
-11.08044627 + 11.08044627 + x = 6.110117954 + 11.08044627

Combine like terms: -11.08044627 + 11.08044627 = 0.00000000
0.00000000 + x = 6.110117954 + 11.08044627
x = 6.110117954 + 11.08044627

Combine like terms: 6.110117954 + 11.08044627 = 17.190564224
x = 17.190564224

Simplifying
x = 17.190564224

Subproblem 2
x + -11.08044627 = -6.110117954

Simplifying
x + -11.08044627 = -6.110117954

Reorder the terms:
-11.08044627 + x = -6.110117954

Solving
-11.08044627 + x = -6.110117954

Solving for variable 'x'.

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

Add '11.08044627' to each side of the equation.
-11.08044627 + 11.08044627 + x = -6.110117954 + 11.08044627

Combine like terms: -11.08044627 + 11.08044627 = 0.00000000
0.00000000 + x = -6.110117954 + 11.08044627
x = -6.110117954 + 11.08044627

Combine like terms: -6.110117954 + 11.08044627 = 4.970328316
x = 4.970328316

Simplifying
x = 4.970328316

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.190564224, 4.970328316}