x^2-22x-14=0

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Solution for x^2-22x-14=0 equation:


Simplifying
x2 + -22x + -14 = 0

Reorder the terms:
-14 + -22x + x2 = 0

Solving
-14 + -22x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -22x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + -22x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -22x + x2 = 0 + 14
-22x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
-22x + x2 = 14

The x term is -22x.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22x + 121 + x2 = 14 + 121

Reorder the terms:
121 + -22x + x2 = 14 + 121

Combine like terms: 14 + 121 = 135
121 + -22x + x2 = 135

Factor a perfect square on the left side:
(x + -11)(x + -11) = 135

Calculate the square root of the right side: 11.618950039

Break this problem into two subproblems by setting 
(x + -11) equal to 11.618950039 and -11.618950039.

Subproblem 1

x + -11 = 11.618950039 Simplifying x + -11 = 11.618950039 Reorder the terms: -11 + x = 11.618950039 Solving -11 + x = 11.618950039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 11.618950039 + 11 Combine like terms: -11 + 11 = 0 0 + x = 11.618950039 + 11 x = 11.618950039 + 11 Combine like terms: 11.618950039 + 11 = 22.618950039 x = 22.618950039 Simplifying x = 22.618950039

Subproblem 2

x + -11 = -11.618950039 Simplifying x + -11 = -11.618950039 Reorder the terms: -11 + x = -11.618950039 Solving -11 + x = -11.618950039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -11.618950039 + 11 Combine like terms: -11 + 11 = 0 0 + x = -11.618950039 + 11 x = -11.618950039 + 11 Combine like terms: -11.618950039 + 11 = -0.618950039 x = -0.618950039 Simplifying x = -0.618950039

Solution

The solution to the problem is based on the solutions from the subproblems. x = {22.618950039, -0.618950039}

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