x^2+45x-66=0

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Solution for x^2+45x-66=0 equation: 


Simplifying
x2 + 45x + -66 = 0

Reorder the terms:
-66 + 45x + x2 = 0

Solving
-66 + 45x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '66' to each side of the equation.
-66 + 45x + 66 + x2 = 0 + 66

Reorder the terms:
-66 + 66 + 45x + x2 = 0 + 66

Combine like terms: -66 + 66 = 0
0 + 45x + x2 = 0 + 66
45x + x2 = 0 + 66

Combine like terms: 0 + 66 = 66
45x + x2 = 66

The x term is 45x.  Take half its coefficient (22.5).
Square it (506.25) and add it to both sides.

Add '506.25' to each side of the equation.
45x + 506.25 + x2 = 66 + 506.25

Reorder the terms:
506.25 + 45x + x2 = 66 + 506.25

Combine like terms: 66 + 506.25 = 572.25
506.25 + 45x + x2 = 572.25

Factor a perfect square on the left side:
(x + 22.5)(x + 22.5) = 572.25

Calculate the square root of the right side: 23.921747428

Break this problem into two subproblems by setting 
(x + 22.5) equal to 23.921747428 and -23.921747428.


Subproblem 1
x + 22.5 = 23.921747428

Simplifying
x + 22.5 = 23.921747428

Reorder the terms:
22.5 + x = 23.921747428

Solving
22.5 + x = 23.921747428

Solving for variable 'x'.

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

Add '-22.5' to each side of the equation.
22.5 + -22.5 + x = 23.921747428 + -22.5

Combine like terms: 22.5 + -22.5 = 0.0
0.0 + x = 23.921747428 + -22.5
x = 23.921747428 + -22.5

Combine like terms: 23.921747428 + -22.5 = 1.421747428
x = 1.421747428

Simplifying
x = 1.421747428


Subproblem 2
x + 22.5 = -23.921747428

Simplifying
x + 22.5 = -23.921747428

Reorder the terms:
22.5 + x = -23.921747428

Solving
22.5 + x = -23.921747428

Solving for variable 'x'.

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

Add '-22.5' to each side of the equation.
22.5 + -22.5 + x = -23.921747428 + -22.5

Combine like terms: 22.5 + -22.5 = 0.0
0.0 + x = -23.921747428 + -22.5
x = -23.921747428 + -22.5

Combine like terms: -23.921747428 + -22.5 = -46.421747428
x = -46.421747428

Simplifying
x = -46.421747428


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.421747428, -46.421747428}

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