1638.25=3.604x^2+27.626x-26.714

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Solution for 1638.25=3.604x^2+27.626x-26.714 equation: 


Simplifying
1638.25 = 3.604x2 + 27.626x + -26.714

Reorder the terms:
1638.25 = -26.714 + 27.626x + 3.604x2

Solving
1638.25 = -26.714 + 27.626x + 3.604x2

Solving for variable 'x'.

Combine like terms: 1638.25 + 26.714 = 1664.964
1664.964 + -27.626x + -3.604x2 = -26.714 + 27.626x + 3.604x2 + 26.714 + -27.626x + -3.604x2

Reorder the terms:
1664.964 + -27.626x + -3.604x2 = -26.714 + 26.714 + 27.626x + -27.626x + 3.604x2 + -3.604x2

Combine like terms: -26.714 + 26.714 = 0.000
1664.964 + -27.626x + -3.604x2 = 0.000 + 27.626x + -27.626x + 3.604x2 + -3.604x2
1664.964 + -27.626x + -3.604x2 = 27.626x + -27.626x + 3.604x2 + -3.604x2

Combine like terms: 27.626x + -27.626x = 0.000
1664.964 + -27.626x + -3.604x2 = 0.000 + 3.604x2 + -3.604x2
1664.964 + -27.626x + -3.604x2 = 3.604x2 + -3.604x2

Combine like terms: 3.604x2 + -3.604x2 = 0.000
1664.964 + -27.626x + -3.604x2 = 0.000

Begin completing the square.  Divide all terms by
-3.604 the coefficient of the squared term: 

Divide each side by '-3.604'.
-461.9766926 + 7.665371809x + x2 = 0

Move the constant term to the right:

Add '461.9766926' to each side of the equation.
-461.9766926 + 7.665371809x + 461.9766926 + x2 = 0 + 461.9766926

Reorder the terms:
-461.9766926 + 461.9766926 + 7.665371809x + x2 = 0 + 461.9766926

Combine like terms: -461.9766926 + 461.9766926 = 0.0000000
0.0000000 + 7.665371809x + x2 = 0 + 461.9766926
7.665371809x + x2 = 0 + 461.9766926

Combine like terms: 0 + 461.9766926 = 461.9766926
7.665371809x + x2 = 461.9766926

The x term is 7.665371809x.  Take half its coefficient (3.832685905).
Square it (14.68948125) and add it to both sides.

Add '14.68948125' to each side of the equation.
7.665371809x + 14.68948125 + x2 = 461.9766926 + 14.68948125

Reorder the terms:
14.68948125 + 7.665371809x + x2 = 461.9766926 + 14.68948125

Combine like terms: 461.9766926 + 14.68948125 = 476.66617385
14.68948125 + 7.665371809x + x2 = 476.66617385

Factor a perfect square on the left side:
(x + 3.832685905)(x + 3.832685905) = 476.66617385

Calculate the square root of the right side: 21.832685906

Break this problem into two subproblems by setting 
(x + 3.832685905) equal to 21.832685906 and -21.832685906.


Subproblem 1
x + 3.832685905 = 21.832685906

Simplifying
x + 3.832685905 = 21.832685906

Reorder the terms:
3.832685905 + x = 21.832685906

Solving
3.832685905 + x = 21.832685906

Solving for variable 'x'.

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

Add '-3.832685905' to each side of the equation.
3.832685905 + -3.832685905 + x = 21.832685906 + -3.832685905

Combine like terms: 3.832685905 + -3.832685905 = 0.000000000
0.000000000 + x = 21.832685906 + -3.832685905
x = 21.832685906 + -3.832685905

Combine like terms: 21.832685906 + -3.832685905 = 18.000000001
x = 18.000000001

Simplifying
x = 18.000000001


Subproblem 2
x + 3.832685905 = -21.832685906

Simplifying
x + 3.832685905 = -21.832685906

Reorder the terms:
3.832685905 + x = -21.832685906

Solving
3.832685905 + x = -21.832685906

Solving for variable 'x'.

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

Add '-3.832685905' to each side of the equation.
3.832685905 + -3.832685905 + x = -21.832685906 + -3.832685905

Combine like terms: 3.832685905 + -3.832685905 = 0.000000000
0.000000000 + x = -21.832685906 + -3.832685905
x = -21.832685906 + -3.832685905

Combine like terms: -21.832685906 + -3.832685905 = -25.665371811
x = -25.665371811

Simplifying
x = -25.665371811


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.000000001, -25.665371811}

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