x^2-10x-67=0

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Solution for x^2-10x-67=0 equation: 


Simplifying
x2 + -10x + -67 = 0

Reorder the terms:
-67 + -10x + x2 = 0

Solving
-67 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '67' to each side of the equation.
-67 + -10x + 67 + x2 = 0 + 67

Reorder the terms:
-67 + 67 + -10x + x2 = 0 + 67

Combine like terms: -67 + 67 = 0
0 + -10x + x2 = 0 + 67
-10x + x2 = 0 + 67

Combine like terms: 0 + 67 = 67
-10x + x2 = 67

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 67 + 25

Reorder the terms:
25 + -10x + x2 = 67 + 25

Combine like terms: 67 + 25 = 92
25 + -10x + x2 = 92

Factor a perfect square on the left side:
(x + -5)(x + -5) = 92

Calculate the square root of the right side: 9.591663047

Break this problem into two subproblems by setting 
(x + -5) equal to 9.591663047 and -9.591663047.


Subproblem 1
x + -5 = 9.591663047

Simplifying
x + -5 = 9.591663047

Reorder the terms:
-5 + x = 9.591663047

Solving
-5 + x = 9.591663047

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 9.591663047 + 5

Combine like terms: -5 + 5 = 0
0 + x = 9.591663047 + 5
x = 9.591663047 + 5

Combine like terms: 9.591663047 + 5 = 14.591663047
x = 14.591663047

Simplifying
x = 14.591663047


Subproblem 2
x + -5 = -9.591663047

Simplifying
x + -5 = -9.591663047

Reorder the terms:
-5 + x = -9.591663047

Solving
-5 + x = -9.591663047

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -9.591663047 + 5

Combine like terms: -5 + 5 = 0
0 + x = -9.591663047 + 5
x = -9.591663047 + 5

Combine like terms: -9.591663047 + 5 = -4.591663047
x = -4.591663047

Simplifying
x = -4.591663047


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.591663047, -4.591663047}

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