x^2-28x-192=0

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Solution for x^2-28x-192=0 equation:


Simplifying
x2 + -28x + -192 = 0

Reorder the terms:
-192 + -28x + x2 = 0

Solving
-192 + -28x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '192' to each side of the equation.
-192 + -28x + 192 + x2 = 0 + 192

Reorder the terms:
-192 + 192 + -28x + x2 = 0 + 192

Combine like terms: -192 + 192 = 0
0 + -28x + x2 = 0 + 192
-28x + x2 = 0 + 192

Combine like terms: 0 + 192 = 192
-28x + x2 = 192

The x term is -28x.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28x + 196 + x2 = 192 + 196

Reorder the terms:
196 + -28x + x2 = 192 + 196

Combine like terms: 192 + 196 = 388
196 + -28x + x2 = 388

Factor a perfect square on the left side:
(x + -14)(x + -14) = 388

Calculate the square root of the right side: 19.697715604

Break this problem into two subproblems by setting 
(x + -14) equal to 19.697715604 and -19.697715604.

Subproblem 1

x + -14 = 19.697715604 Simplifying x + -14 = 19.697715604 Reorder the terms: -14 + x = 19.697715604 Solving -14 + x = 19.697715604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 19.697715604 + 14 Combine like terms: -14 + 14 = 0 0 + x = 19.697715604 + 14 x = 19.697715604 + 14 Combine like terms: 19.697715604 + 14 = 33.697715604 x = 33.697715604 Simplifying x = 33.697715604

Subproblem 2

x + -14 = -19.697715604 Simplifying x + -14 = -19.697715604 Reorder the terms: -14 + x = -19.697715604 Solving -14 + x = -19.697715604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -19.697715604 + 14 Combine like terms: -14 + 14 = 0 0 + x = -19.697715604 + 14 x = -19.697715604 + 14 Combine like terms: -19.697715604 + 14 = -5.697715604 x = -5.697715604 Simplifying x = -5.697715604

Solution

The solution to the problem is based on the solutions from the subproblems. x = {33.697715604, -5.697715604}

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