x^2-9x+7.25=0

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Solution for x^2-9x+7.25=0 equation: 


Simplifying
x2 + -9x + 7.25 = 0

Reorder the terms:
7.25 + -9x + x2 = 0

Solving
7.25 + -9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-7.25' to each side of the equation.
7.25 + -9x + -7.25 + x2 = 0 + -7.25

Reorder the terms:
7.25 + -7.25 + -9x + x2 = 0 + -7.25

Combine like terms: 7.25 + -7.25 = 0.00
0.00 + -9x + x2 = 0 + -7.25
-9x + x2 = 0 + -7.25

Combine like terms: 0 + -7.25 = -7.25
-9x + x2 = -7.25

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -7.25 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -7.25 + 20.25

Combine like terms: -7.25 + 20.25 = 13
20.25 + -9x + x2 = 13

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + -4.5) equal to 3.605551275 and -3.605551275.


Subproblem 1
x + -4.5 = 3.605551275

Simplifying
x + -4.5 = 3.605551275

Reorder the terms:
-4.5 + x = 3.605551275

Solving
-4.5 + x = 3.605551275

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 3.605551275 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 3.605551275 + 4.5
x = 3.605551275 + 4.5

Combine like terms: 3.605551275 + 4.5 = 8.105551275
x = 8.105551275

Simplifying
x = 8.105551275


Subproblem 2
x + -4.5 = -3.605551275

Simplifying
x + -4.5 = -3.605551275

Reorder the terms:
-4.5 + x = -3.605551275

Solving
-4.5 + x = -3.605551275

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -3.605551275 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -3.605551275 + 4.5
x = -3.605551275 + 4.5

Combine like terms: -3.605551275 + 4.5 = 0.894448725
x = 0.894448725

Simplifying
x = 0.894448725


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.105551275, 0.894448725}

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