x^2-3.71x-16.9=0

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Solution for x^2-3.71x-16.9=0 equation: 


Simplifying
x2 + -3.71x + -16.9 = 0

Reorder the terms:
-16.9 + -3.71x + x2 = 0

Solving
-16.9 + -3.71x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '16.9' to each side of the equation.
-16.9 + -3.71x + 16.9 + x2 = 0 + 16.9

Reorder the terms:
-16.9 + 16.9 + -3.71x + x2 = 0 + 16.9

Combine like terms: -16.9 + 16.9 = 0.0
0.0 + -3.71x + x2 = 0 + 16.9
-3.71x + x2 = 0 + 16.9

Combine like terms: 0 + 16.9 = 16.9
-3.71x + x2 = 16.9

The x term is -3.71x.  Take half its coefficient (-1.855).
Square it (3.441025) and add it to both sides.

Add '3.441025' to each side of the equation.
-3.71x + 3.441025 + x2 = 16.9 + 3.441025

Reorder the terms:
3.441025 + -3.71x + x2 = 16.9 + 3.441025

Combine like terms: 16.9 + 3.441025 = 20.341025
3.441025 + -3.71x + x2 = 20.341025

Factor a perfect square on the left side:
(x + -1.855)(x + -1.855) = 20.341025

Calculate the square root of the right side: 4.510102549

Break this problem into two subproblems by setting 
(x + -1.855) equal to 4.510102549 and -4.510102549.


Subproblem 1
x + -1.855 = 4.510102549

Simplifying
x + -1.855 = 4.510102549

Reorder the terms:
-1.855 + x = 4.510102549

Solving
-1.855 + x = 4.510102549

Solving for variable 'x'.

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

Add '1.855' to each side of the equation.
-1.855 + 1.855 + x = 4.510102549 + 1.855

Combine like terms: -1.855 + 1.855 = 0.000
0.000 + x = 4.510102549 + 1.855
x = 4.510102549 + 1.855

Combine like terms: 4.510102549 + 1.855 = 6.365102549
x = 6.365102549

Simplifying
x = 6.365102549


Subproblem 2
x + -1.855 = -4.510102549

Simplifying
x + -1.855 = -4.510102549

Reorder the terms:
-1.855 + x = -4.510102549

Solving
-1.855 + x = -4.510102549

Solving for variable 'x'.

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

Add '1.855' to each side of the equation.
-1.855 + 1.855 + x = -4.510102549 + 1.855

Combine like terms: -1.855 + 1.855 = 0.000
0.000 + x = -4.510102549 + 1.855
x = -4.510102549 + 1.855

Combine like terms: -4.510102549 + 1.855 = -2.655102549
x = -2.655102549

Simplifying
x = -2.655102549


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.365102549, -2.655102549}

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