x^2-5x=-3.25

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Solution for x^2-5x=-3.25 equation: 


Simplifying
x2 + -5x = -3.25

Reorder the terms:
-5x + x2 = -3.25

Solving
-5x + x2 = -3.25

Solving for variable 'x'.

Reorder the terms:
3.25 + -5x + x2 = -3.25 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
3.25 + -5x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '-3.25' to each side of the equation.
3.25 + -5x + -3.25 + x2 = 0.00 + -3.25

Reorder the terms:
3.25 + -3.25 + -5x + x2 = 0.00 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + -5x + x2 = 0.00 + -3.25
-5x + x2 = 0.00 + -3.25

Combine like terms: 0.00 + -3.25 = -3.25
-5x + x2 = -3.25

The x term is -5x.  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.
-5x + 6.25 + x2 = -3.25 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -3.25 + 6.25

Combine like terms: -3.25 + 6.25 = 3
6.25 + -5x + x2 = 3

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.732050808 and -1.732050808.


Subproblem 1
x + -2.5 = 1.732050808

Simplifying
x + -2.5 = 1.732050808

Reorder the terms:
-2.5 + x = 1.732050808

Solving
-2.5 + x = 1.732050808

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 = 1.732050808 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 1.732050808 + 2.5
x = 1.732050808 + 2.5

Combine like terms: 1.732050808 + 2.5 = 4.232050808
x = 4.232050808

Simplifying
x = 4.232050808


Subproblem 2
x + -2.5 = -1.732050808

Simplifying
x + -2.5 = -1.732050808

Reorder the terms:
-2.5 + x = -1.732050808

Solving
-2.5 + x = -1.732050808

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 = -1.732050808 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -1.732050808 + 2.5
x = -1.732050808 + 2.5

Combine like terms: -1.732050808 + 2.5 = 0.767949192
x = 0.767949192

Simplifying
x = 0.767949192


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.232050808, 0.767949192}

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