x^2-4.5x-50=0

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Solution for x^2-4.5x-50=0 equation: 


Simplifying
x2 + -4.5x + -50 = 0

Reorder the terms:
-50 + -4.5x + x2 = 0

Solving
-50 + -4.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + -4.5x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + -4.5x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -4.5x + x2 = 0 + 50
-4.5x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
-4.5x + x2 = 50

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 = 50 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 50 + 5.0625

Combine like terms: 50 + 5.0625 = 55.0625
5.0625 + -4.5x + x2 = 55.0625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 55.0625

Calculate the square root of the right side: 7.42041104

Break this problem into two subproblems by setting 
(x + -2.25) equal to 7.42041104 and -7.42041104.


Subproblem 1
x + -2.25 = 7.42041104

Simplifying
x + -2.25 = 7.42041104

Reorder the terms:
-2.25 + x = 7.42041104

Solving
-2.25 + x = 7.42041104

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 = 7.42041104 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 7.42041104 + 2.25
x = 7.42041104 + 2.25

Combine like terms: 7.42041104 + 2.25 = 9.67041104
x = 9.67041104

Simplifying
x = 9.67041104


Subproblem 2
x + -2.25 = -7.42041104

Simplifying
x + -2.25 = -7.42041104

Reorder the terms:
-2.25 + x = -7.42041104

Solving
-2.25 + x = -7.42041104

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 = -7.42041104 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -7.42041104 + 2.25
x = -7.42041104 + 2.25

Combine like terms: -7.42041104 + 2.25 = -5.17041104
x = -5.17041104

Simplifying
x = -5.17041104


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.67041104, -5.17041104}

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