x^2-4x-19.25=0

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Solution for x^2-4x-19.25=0 equation: 


Simplifying
x2 + -4x + -19.25 = 0

Reorder the terms:
-19.25 + -4x + x2 = 0

Solving
-19.25 + -4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '19.25' to each side of the equation.
-19.25 + -4x + 19.25 + x2 = 0 + 19.25

Reorder the terms:
-19.25 + 19.25 + -4x + x2 = 0 + 19.25

Combine like terms: -19.25 + 19.25 = 0.00
0.00 + -4x + x2 = 0 + 19.25
-4x + x2 = 0 + 19.25

Combine like terms: 0 + 19.25 = 19.25
-4x + x2 = 19.25

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 19.25 + 4

Reorder the terms:
4 + -4x + x2 = 19.25 + 4

Combine like terms: 19.25 + 4 = 23.25
4 + -4x + x2 = 23.25

Factor a perfect square on the left side:
(x + -2)(x + -2) = 23.25

Calculate the square root of the right side: 4.82182538

Break this problem into two subproblems by setting 
(x + -2) equal to 4.82182538 and -4.82182538.


Subproblem 1
x + -2 = 4.82182538

Simplifying
x + -2 = 4.82182538

Reorder the terms:
-2 + x = 4.82182538

Solving
-2 + x = 4.82182538

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 4.82182538 + 2

Combine like terms: -2 + 2 = 0
0 + x = 4.82182538 + 2
x = 4.82182538 + 2

Combine like terms: 4.82182538 + 2 = 6.82182538
x = 6.82182538

Simplifying
x = 6.82182538


Subproblem 2
x + -2 = -4.82182538

Simplifying
x + -2 = -4.82182538

Reorder the terms:
-2 + x = -4.82182538

Solving
-2 + x = -4.82182538

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -4.82182538 + 2

Combine like terms: -2 + 2 = 0
0 + x = -4.82182538 + 2
x = -4.82182538 + 2

Combine like terms: -4.82182538 + 2 = -2.82182538
x = -2.82182538

Simplifying
x = -2.82182538


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.82182538, -2.82182538}

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