x^2-6.5x-34=0

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Solution for x^2-6.5x-34=0 equation: 


Simplifying
x2 + -6.5x + -34 = 0

Reorder the terms:
-34 + -6.5x + x2 = 0

Solving
-34 + -6.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '34' to each side of the equation.
-34 + -6.5x + 34 + x2 = 0 + 34

Reorder the terms:
-34 + 34 + -6.5x + x2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + -6.5x + x2 = 0 + 34
-6.5x + x2 = 0 + 34

Combine like terms: 0 + 34 = 34
-6.5x + x2 = 34

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 = 34 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = 34 + 10.5625

Combine like terms: 34 + 10.5625 = 44.5625
10.5625 + -6.5x + x2 = 44.5625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 44.5625

Calculate the square root of the right side: 6.675514961

Break this problem into two subproblems by setting 
(x + -3.25) equal to 6.675514961 and -6.675514961.


Subproblem 1
x + -3.25 = 6.675514961

Simplifying
x + -3.25 = 6.675514961

Reorder the terms:
-3.25 + x = 6.675514961

Solving
-3.25 + x = 6.675514961

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 = 6.675514961 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = 6.675514961 + 3.25
x = 6.675514961 + 3.25

Combine like terms: 6.675514961 + 3.25 = 9.925514961
x = 9.925514961

Simplifying
x = 9.925514961


Subproblem 2
x + -3.25 = -6.675514961

Simplifying
x + -3.25 = -6.675514961

Reorder the terms:
-3.25 + x = -6.675514961

Solving
-3.25 + x = -6.675514961

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 = -6.675514961 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + x = -6.675514961 + 3.25
x = -6.675514961 + 3.25

Combine like terms: -6.675514961 + 3.25 = -3.425514961
x = -3.425514961

Simplifying
x = -3.425514961


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.925514961, -3.425514961}

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