x^2-47.74x=1636.8

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Solution for x^2-47.74x=1636.8 equation: 


Simplifying
x2 + -47.74x = 1636.8

Reorder the terms:
-47.74x + x2 = 1636.8

Solving
-47.74x + x2 = 1636.8

Solving for variable 'x'.

Reorder the terms:
-1636.8 + -47.74x + x2 = 1636.8 + -1636.8

Combine like terms: 1636.8 + -1636.8 = 0.0
-1636.8 + -47.74x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '1636.8' to each side of the equation.
-1636.8 + -47.74x + 1636.8 + x2 = 0.0 + 1636.8

Reorder the terms:
-1636.8 + 1636.8 + -47.74x + x2 = 0.0 + 1636.8

Combine like terms: -1636.8 + 1636.8 = 0.0
0.0 + -47.74x + x2 = 0.0 + 1636.8
-47.74x + x2 = 0.0 + 1636.8

Combine like terms: 0.0 + 1636.8 = 1636.8
-47.74x + x2 = 1636.8

The x term is -47.74x.  Take half its coefficient (-23.87).
Square it (569.7769) and add it to both sides.

Add '569.7769' to each side of the equation.
-47.74x + 569.7769 + x2 = 1636.8 + 569.7769

Reorder the terms:
569.7769 + -47.74x + x2 = 1636.8 + 569.7769

Combine like terms: 1636.8 + 569.7769 = 2206.5769
569.7769 + -47.74x + x2 = 2206.5769

Factor a perfect square on the left side:
(x + -23.87)(x + -23.87) = 2206.5769

Calculate the square root of the right side: 46.974215268

Break this problem into two subproblems by setting 
(x + -23.87) equal to 46.974215268 and -46.974215268.


Subproblem 1
x + -23.87 = 46.974215268

Simplifying
x + -23.87 = 46.974215268

Reorder the terms:
-23.87 + x = 46.974215268

Solving
-23.87 + x = 46.974215268

Solving for variable 'x'.

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

Add '23.87' to each side of the equation.
-23.87 + 23.87 + x = 46.974215268 + 23.87

Combine like terms: -23.87 + 23.87 = 0.00
0.00 + x = 46.974215268 + 23.87
x = 46.974215268 + 23.87

Combine like terms: 46.974215268 + 23.87 = 70.844215268
x = 70.844215268

Simplifying
x = 70.844215268


Subproblem 2
x + -23.87 = -46.974215268

Simplifying
x + -23.87 = -46.974215268

Reorder the terms:
-23.87 + x = -46.974215268

Solving
-23.87 + x = -46.974215268

Solving for variable 'x'.

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

Add '23.87' to each side of the equation.
-23.87 + 23.87 + x = -46.974215268 + 23.87

Combine like terms: -23.87 + 23.87 = 0.00
0.00 + x = -46.974215268 + 23.87
x = -46.974215268 + 23.87

Combine like terms: -46.974215268 + 23.87 = -23.104215268
x = -23.104215268

Simplifying
x = -23.104215268


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {70.844215268, -23.104215268}

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