0=x^2+9x+16.25

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Solution for 0=x^2+9x+16.25 equation: 


Simplifying
0 = x2 + 9x + 16.25

Reorder the terms:
0 = 16.25 + 9x + x2

Solving
0 = 16.25 + 9x + x2

Solving for variable 'x'.

Combine like terms: 0 + -16.25 = -16.25
-16.25 + -9x + -1x2 = 16.25 + 9x + x2 + -16.25 + -9x + -1x2

Reorder the terms:
-16.25 + -9x + -1x2 = 16.25 + -16.25 + 9x + -9x + x2 + -1x2

Combine like terms: 16.25 + -16.25 = 0.00
-16.25 + -9x + -1x2 = 0.00 + 9x + -9x + x2 + -1x2
-16.25 + -9x + -1x2 = 9x + -9x + x2 + -1x2

Combine like terms: 9x + -9x = 0
-16.25 + -9x + -1x2 = 0 + x2 + -1x2
-16.25 + -9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-16.25 + -9x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
16.25 + 9x + x2 = 0

Move the constant term to the right:

Add '-16.25' to each side of the equation.
16.25 + 9x + -16.25 + x2 = 0 + -16.25

Reorder the terms:
16.25 + -16.25 + 9x + x2 = 0 + -16.25

Combine like terms: 16.25 + -16.25 = 0.00
0.00 + 9x + x2 = 0 + -16.25
9x + x2 = 0 + -16.25

Combine like terms: 0 + -16.25 = -16.25
9x + x2 = -16.25

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 = -16.25 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -16.25 + 20.25

Combine like terms: -16.25 + 20.25 = 4
20.25 + 9x + x2 = 4

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(x + 4.5) equal to 2 and -2.


Subproblem 1
x + 4.5 = 2

Simplifying
x + 4.5 = 2

Reorder the terms:
4.5 + x = 2

Solving
4.5 + x = 2

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 = 2 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 2 + -4.5
x = 2 + -4.5

Combine like terms: 2 + -4.5 = -2.5
x = -2.5

Simplifying
x = -2.5


Subproblem 2
x + 4.5 = -2

Simplifying
x + 4.5 = -2

Reorder the terms:
4.5 + x = -2

Solving
4.5 + x = -2

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 = -2 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -2 + -4.5
x = -2 + -4.5

Combine like terms: -2 + -4.5 = -6.5
x = -6.5

Simplifying
x = -6.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.5, -6.5}

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