x^2-6x-9.75=0

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Solution for x^2-6x-9.75=0 equation: 


Simplifying
x2 + -6x + -9.75 = 0

Reorder the terms:
-9.75 + -6x + x2 = 0

Solving
-9.75 + -6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '9.75' to each side of the equation.
-9.75 + -6x + 9.75 + x2 = 0 + 9.75

Reorder the terms:
-9.75 + 9.75 + -6x + x2 = 0 + 9.75

Combine like terms: -9.75 + 9.75 = 0.00
0.00 + -6x + x2 = 0 + 9.75
-6x + x2 = 0 + 9.75

Combine like terms: 0 + 9.75 = 9.75
-6x + x2 = 9.75

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 9.75 + 9

Reorder the terms:
9 + -6x + x2 = 9.75 + 9

Combine like terms: 9.75 + 9 = 18.75
9 + -6x + x2 = 18.75

Factor a perfect square on the left side:
(x + -3)(x + -3) = 18.75

Calculate the square root of the right side: 4.330127019

Break this problem into two subproblems by setting 
(x + -3) equal to 4.330127019 and -4.330127019.


Subproblem 1
x + -3 = 4.330127019

Simplifying
x + -3 = 4.330127019

Reorder the terms:
-3 + x = 4.330127019

Solving
-3 + x = 4.330127019

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 4.330127019 + 3

Combine like terms: -3 + 3 = 0
0 + x = 4.330127019 + 3
x = 4.330127019 + 3

Combine like terms: 4.330127019 + 3 = 7.330127019
x = 7.330127019

Simplifying
x = 7.330127019


Subproblem 2
x + -3 = -4.330127019

Simplifying
x + -3 = -4.330127019

Reorder the terms:
-3 + x = -4.330127019

Solving
-3 + x = -4.330127019

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -4.330127019 + 3

Combine like terms: -3 + 3 = 0
0 + x = -4.330127019 + 3
x = -4.330127019 + 3

Combine like terms: -4.330127019 + 3 = -1.330127019
x = -1.330127019

Simplifying
x = -1.330127019


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.330127019, -1.330127019}

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