x^2-6.5x-42=0

Solution for x^2-6.5x-42=0 equation:

Simplifying
x2 + -6.5x + -42 = 0

Reorder the terms:
-42 + -6.5x + x2 = 0

Solving
-42 + -6.5x + 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 + -6.5x + 42 + x2 = 0 + 42

Reorder the terms:
-42 + 42 + -6.5x + x2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + -6.5x + x2 = 0 + 42
-6.5x + x2 = 0 + 42

Combine like terms: 0 + 42 = 42
-6.5x + x2 = 42

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = 42 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = 42 + 10.5625

Combine like terms: 42 + 10.5625 = 52.5625
10.5625 + -6.5x + x2 = 52.5625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 52.5625

Calculate the square root of the right side: 7.25

Break this problem into two subproblems by setting 
(x + -3.25) equal to 7.25 and -7.25.

Subproblem 1
x + -3.25 = 7.25

Simplifying
x + -3.25 = 7.25

Reorder the terms:
-3.25 + x = 7.25

Solving
-3.25 + x = 7.25

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = 7.25 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = 7.25 + 3.25
x = 7.25 + 3.25

Combine like terms: 7.25 + 3.25 = 10.5
x = 10.5

Simplifying
x = 10.5

Subproblem 2
x + -3.25 = -7.25

Simplifying
x + -3.25 = -7.25

Reorder the terms:
-3.25 + x = -7.25

Solving
-3.25 + x = -7.25

Solving for variable 'x'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + x = -7.25 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = -7.25 + 3.25
x = -7.25 + 3.25

Combine like terms: -7.25 + 3.25 = -4
x = -4

Simplifying
x = -4

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.5, -4}