x^2+9x-1.75=0

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Solution for x^2+9x-1.75=0 equation: 


Simplifying
x2 + 9x + -1.75 = 0

Reorder the terms:
-1.75 + 9x + x2 = 0

Solving
-1.75 + 9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1.75' to each side of the equation.
-1.75 + 9x + 1.75 + x2 = 0 + 1.75

Reorder the terms:
-1.75 + 1.75 + 9x + x2 = 0 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + 9x + x2 = 0 + 1.75
9x + x2 = 0 + 1.75

Combine like terms: 0 + 1.75 = 1.75
9x + x2 = 1.75

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 = 1.75 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 1.75 + 20.25

Combine like terms: 1.75 + 20.25 = 22
20.25 + 9x + x2 = 22

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(x + 4.5) equal to 4.69041576 and -4.69041576.


Subproblem 1
x + 4.5 = 4.69041576

Simplifying
x + 4.5 = 4.69041576

Reorder the terms:
4.5 + x = 4.69041576

Solving
4.5 + x = 4.69041576

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 = 4.69041576 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 4.69041576 + -4.5
x = 4.69041576 + -4.5

Combine like terms: 4.69041576 + -4.5 = 0.19041576
x = 0.19041576

Simplifying
x = 0.19041576


Subproblem 2
x + 4.5 = -4.69041576

Simplifying
x + 4.5 = -4.69041576

Reorder the terms:
4.5 + x = -4.69041576

Solving
4.5 + x = -4.69041576

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 = -4.69041576 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -4.69041576 + -4.5
x = -4.69041576 + -4.5

Combine like terms: -4.69041576 + -4.5 = -9.19041576
x = -9.19041576

Simplifying
x = -9.19041576


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.19041576, -9.19041576}

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