x^2-6x-34=0

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Solution for x^2-6x-34=0 equation:


Simplifying
x2 + -6x + -34 = 0

Reorder the terms:
-34 + -6x + x2 = 0

Solving
-34 + -6x + 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 + -6x + 34 + x2 = 0 + 34

Reorder the terms:
-34 + 34 + -6x + x2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + -6x + x2 = 0 + 34
-6x + x2 = 0 + 34

Combine like terms: 0 + 34 = 34
-6x + x2 = 34

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 = 34 + 9

Reorder the terms:
9 + -6x + x2 = 34 + 9

Combine like terms: 34 + 9 = 43
9 + -6x + x2 = 43

Factor a perfect square on the left side:
(x + -3)(x + -3) = 43

Calculate the square root of the right side: 6.557438524

Break this problem into two subproblems by setting 
(x + -3) equal to 6.557438524 and -6.557438524.

Subproblem 1

x + -3 = 6.557438524 Simplifying x + -3 = 6.557438524 Reorder the terms: -3 + x = 6.557438524 Solving -3 + x = 6.557438524 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 = 6.557438524 + 3 Combine like terms: -3 + 3 = 0 0 + x = 6.557438524 + 3 x = 6.557438524 + 3 Combine like terms: 6.557438524 + 3 = 9.557438524 x = 9.557438524 Simplifying x = 9.557438524

Subproblem 2

x + -3 = -6.557438524 Simplifying x + -3 = -6.557438524 Reorder the terms: -3 + x = -6.557438524 Solving -3 + x = -6.557438524 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 = -6.557438524 + 3 Combine like terms: -3 + 3 = 0 0 + x = -6.557438524 + 3 x = -6.557438524 + 3 Combine like terms: -6.557438524 + 3 = -3.557438524 x = -3.557438524 Simplifying x = -3.557438524

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.557438524, -3.557438524}

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