x^2-19.0x=9.75

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Solution for x^2-19.0x=9.75 equation: 


Simplifying
x2 + -19.0x = 9.75

Reorder the terms:
-19.0x + x2 = 9.75

Solving
-19.0x + x2 = 9.75

Solving for variable 'x'.

Reorder the terms:
-9.75 + -19.0x + x2 = 9.75 + -9.75

Combine like terms: 9.75 + -9.75 = 0.00
-9.75 + -19.0x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '9.75' to each side of the equation.
-9.75 + -19.0x + 9.75 + x2 = 0.00 + 9.75

Reorder the terms:
-9.75 + 9.75 + -19.0x + x2 = 0.00 + 9.75

Combine like terms: -9.75 + 9.75 = 0.00
0.00 + -19.0x + x2 = 0.00 + 9.75
-19.0x + x2 = 0.00 + 9.75

Combine like terms: 0.00 + 9.75 = 9.75
-19.0x + x2 = 9.75

The x term is -19.0x.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19.0x + 90.25 + x2 = 9.75 + 90.25

Reorder the terms:
90.25 + -19.0x + x2 = 9.75 + 90.25

Combine like terms: 9.75 + 90.25 = 100
90.25 + -19.0x + x2 = 100

Factor a perfect square on the left side:
(x + -9.5)(x + -9.5) = 100

Calculate the square root of the right side: 10

Break this problem into two subproblems by setting 
(x + -9.5) equal to 10 and -10.


Subproblem 1
x + -9.5 = 10

Simplifying
x + -9.5 = 10

Reorder the terms:
-9.5 + x = 10

Solving
-9.5 + x = 10

Solving for variable 'x'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + x = 10 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = 10 + 9.5
x = 10 + 9.5

Combine like terms: 10 + 9.5 = 19.5
x = 19.5

Simplifying
x = 19.5


Subproblem 2
x + -9.5 = -10

Simplifying
x + -9.5 = -10

Reorder the terms:
-9.5 + x = -10

Solving
-9.5 + x = -10

Solving for variable 'x'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + x = -10 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = -10 + 9.5
x = -10 + 9.5

Combine like terms: -10 + 9.5 = -0.5
x = -0.5

Simplifying
x = -0.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.5, -0.5}

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