x^2-6x-19=0

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Solution for x^2-6x-19=0 equation:


Simplifying
x2 + -6x + -19 = 0

Reorder the terms:
-19 + -6x + x2 = 0

Solving
-19 + -6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + -6x + 19 + x2 = 0 + 19

Reorder the terms:
-19 + 19 + -6x + x2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -6x + x2 = 0 + 19
-6x + x2 = 0 + 19

Combine like terms: 0 + 19 = 19
-6x + x2 = 19

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 19 + 9

Reorder the terms:
9 + -6x + x2 = 19 + 9

Combine like terms: 19 + 9 = 28
9 + -6x + x2 = 28

Factor a perfect square on the left side:
(x + -3)(x + -3) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(x + -3) equal to 5.291502622 and -5.291502622.

Subproblem 1

x + -3 = 5.291502622 Simplifying x + -3 = 5.291502622 Reorder the terms: -3 + x = 5.291502622 Solving -3 + x = 5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 5.291502622 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.291502622 + 3 x = 5.291502622 + 3 Combine like terms: 5.291502622 + 3 = 8.291502622 x = 8.291502622 Simplifying x = 8.291502622

Subproblem 2

x + -3 = -5.291502622 Simplifying x + -3 = -5.291502622 Reorder the terms: -3 + x = -5.291502622 Solving -3 + x = -5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -5.291502622 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.291502622 + 3 x = -5.291502622 + 3 Combine like terms: -5.291502622 + 3 = -2.291502622 x = -2.291502622 Simplifying x = -2.291502622

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.291502622, -2.291502622}

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