x^2-4.5x-11.25=0

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Solution for x^2-4.5x-11.25=0 equation: 


Simplifying
x2 + -4.5x + -11.25 = 0

Reorder the terms:
-11.25 + -4.5x + x2 = 0

Solving
-11.25 + -4.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '11.25' to each side of the equation.
-11.25 + -4.5x + 11.25 + x2 = 0 + 11.25

Reorder the terms:
-11.25 + 11.25 + -4.5x + x2 = 0 + 11.25

Combine like terms: -11.25 + 11.25 = 0.00
0.00 + -4.5x + x2 = 0 + 11.25
-4.5x + x2 = 0 + 11.25

Combine like terms: 0 + 11.25 = 11.25
-4.5x + x2 = 11.25

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 11.25 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 11.25 + 5.0625

Combine like terms: 11.25 + 5.0625 = 16.3125
5.0625 + -4.5x + x2 = 16.3125

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 16.3125

Calculate the square root of the right side: 4.038873605

Break this problem into two subproblems by setting 
(x + -2.25) equal to 4.038873605 and -4.038873605.


Subproblem 1
x + -2.25 = 4.038873605

Simplifying
x + -2.25 = 4.038873605

Reorder the terms:
-2.25 + x = 4.038873605

Solving
-2.25 + x = 4.038873605

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = 4.038873605 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 4.038873605 + 2.25
x = 4.038873605 + 2.25

Combine like terms: 4.038873605 + 2.25 = 6.288873605
x = 6.288873605

Simplifying
x = 6.288873605


Subproblem 2
x + -2.25 = -4.038873605

Simplifying
x + -2.25 = -4.038873605

Reorder the terms:
-2.25 + x = -4.038873605

Solving
-2.25 + x = -4.038873605

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = -4.038873605 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -4.038873605 + 2.25
x = -4.038873605 + 2.25

Combine like terms: -4.038873605 + 2.25 = -1.788873605
x = -1.788873605

Simplifying
x = -1.788873605


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.288873605, -1.788873605}

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