x^2-5.0x=9.75

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Solution for x^2-5.0x=9.75 equation: 


Simplifying
x2 + -5.0x = 9.75

Reorder the terms:
-5.0x + x2 = 9.75

Solving
-5.0x + x2 = 9.75

Solving for variable 'x'.

Reorder the terms:
-9.75 + -5.0x + x2 = 9.75 + -9.75

Combine like terms: 9.75 + -9.75 = 0.00
-9.75 + -5.0x + 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 + -5.0x + 9.75 + x2 = 0.00 + 9.75

Reorder the terms:
-9.75 + 9.75 + -5.0x + x2 = 0.00 + 9.75

Combine like terms: -9.75 + 9.75 = 0.00
0.00 + -5.0x + x2 = 0.00 + 9.75
-5.0x + x2 = 0.00 + 9.75

Combine like terms: 0.00 + 9.75 = 9.75
-5.0x + x2 = 9.75

The x term is -5.0x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5.0x + 6.25 + x2 = 9.75 + 6.25

Reorder the terms:
6.25 + -5.0x + x2 = 9.75 + 6.25

Combine like terms: 9.75 + 6.25 = 16
6.25 + -5.0x + x2 = 16

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 16

Calculate the square root of the right side: 4

Break this problem into two subproblems by setting 
(x + -2.5) equal to 4 and -4.


Subproblem 1
x + -2.5 = 4

Simplifying
x + -2.5 = 4

Reorder the terms:
-2.5 + x = 4

Solving
-2.5 + x = 4

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 4 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 4 + 2.5
x = 4 + 2.5

Combine like terms: 4 + 2.5 = 6.5
x = 6.5

Simplifying
x = 6.5


Subproblem 2
x + -2.5 = -4

Simplifying
x + -2.5 = -4

Reorder the terms:
-2.5 + x = -4

Solving
-2.5 + x = -4

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -4 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -4 + 2.5
x = -4 + 2.5

Combine like terms: -4 + 2.5 = -1.5
x = -1.5

Simplifying
x = -1.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.5, -1.5}

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