x^2-45x-42=0

Solution for x^2-45x-42=0 equation:

Simplifying
x2 + -45x + -42 = 0

Reorder the terms:
-42 + -45x + x2 = 0

Solving
-42 + -45x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + -45x + 42 + x2 = 0 + 42

Reorder the terms:
-42 + 42 + -45x + x2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + -45x + x2 = 0 + 42
-45x + x2 = 0 + 42

Combine like terms: 0 + 42 = 42
-45x + x2 = 42

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 = 42 + 506.25

Reorder the terms:
506.25 + -45x + x2 = 42 + 506.25

Combine like terms: 42 + 506.25 = 548.25
506.25 + -45x + x2 = 548.25

Factor a perfect square on the left side:
(x + -22.5)(x + -22.5) = 548.25

Calculate the square root of the right side: 23.414738948

Break this problem into two subproblems by setting 
(x + -22.5) equal to 23.414738948 and -23.414738948.

Subproblem 1
x + -22.5 = 23.414738948

Simplifying
x + -22.5 = 23.414738948

Reorder the terms:
-22.5 + x = 23.414738948

Solving
-22.5 + x = 23.414738948

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 = 23.414738948 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + x = 23.414738948 + 22.5
x = 23.414738948 + 22.5

Combine like terms: 23.414738948 + 22.5 = 45.914738948
x = 45.914738948

Simplifying
x = 45.914738948

Subproblem 2
x + -22.5 = -23.414738948

Simplifying
x + -22.5 = -23.414738948

Reorder the terms:
-22.5 + x = -23.414738948

Solving
-22.5 + x = -23.414738948

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 = -23.414738948 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + x = -23.414738948 + 22.5
x = -23.414738948 + 22.5

Combine like terms: -23.414738948 + 22.5 = -0.914738948
x = -0.914738948

Simplifying
x = -0.914738948

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {45.914738948, -0.914738948}