x^2+9x-4.75=0

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Solution for x^2+9x-4.75=0 equation: 


Simplifying
x2 + 9x + -4.75 = 0

Reorder the terms:
-4.75 + 9x + x2 = 0

Solving
-4.75 + 9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '4.75' to each side of the equation.
-4.75 + 9x + 4.75 + x2 = 0 + 4.75

Reorder the terms:
-4.75 + 4.75 + 9x + x2 = 0 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + 9x + x2 = 0 + 4.75
9x + x2 = 0 + 4.75

Combine like terms: 0 + 4.75 = 4.75
9x + x2 = 4.75

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 = 4.75 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 4.75 + 20.25

Combine like terms: 4.75 + 20.25 = 25
20.25 + 9x + x2 = 25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 25

Calculate the square root of the right side: 5

Break this problem into two subproblems by setting 
(x + 4.5) equal to 5 and -5.


Subproblem 1
x + 4.5 = 5

Simplifying
x + 4.5 = 5

Reorder the terms:
4.5 + x = 5

Solving
4.5 + x = 5

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 = 5 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 5 + -4.5
x = 5 + -4.5

Combine like terms: 5 + -4.5 = 0.5
x = 0.5

Simplifying
x = 0.5


Subproblem 2
x + 4.5 = -5

Simplifying
x + 4.5 = -5

Reorder the terms:
4.5 + x = -5

Solving
4.5 + x = -5

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 = -5 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -5 + -4.5
x = -5 + -4.5

Combine like terms: -5 + -4.5 = -9.5
x = -9.5

Simplifying
x = -9.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5, -9.5}

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