x^2-28x+11=0

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Solution for x^2-28x+11=0 equation:


Simplifying
x2 + -28x + 11 = 0

Reorder the terms:
11 + -28x + x2 = 0

Solving
11 + -28x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -28x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + -28x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -28x + x2 = 0 + -11
-28x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
-28x + x2 = -11

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 = -11 + 196

Reorder the terms:
196 + -28x + x2 = -11 + 196

Combine like terms: -11 + 196 = 185
196 + -28x + x2 = 185

Factor a perfect square on the left side:
(x + -14)(x + -14) = 185

Calculate the square root of the right side: 13.601470509

Break this problem into two subproblems by setting 
(x + -14) equal to 13.601470509 and -13.601470509.

Subproblem 1

x + -14 = 13.601470509 Simplifying x + -14 = 13.601470509 Reorder the terms: -14 + x = 13.601470509 Solving -14 + x = 13.601470509 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 = 13.601470509 + 14 Combine like terms: -14 + 14 = 0 0 + x = 13.601470509 + 14 x = 13.601470509 + 14 Combine like terms: 13.601470509 + 14 = 27.601470509 x = 27.601470509 Simplifying x = 27.601470509

Subproblem 2

x + -14 = -13.601470509 Simplifying x + -14 = -13.601470509 Reorder the terms: -14 + x = -13.601470509 Solving -14 + x = -13.601470509 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 = -13.601470509 + 14 Combine like terms: -14 + 14 = 0 0 + x = -13.601470509 + 14 x = -13.601470509 + 14 Combine like terms: -13.601470509 + 14 = 0.398529491 x = 0.398529491 Simplifying x = 0.398529491

Solution

The solution to the problem is based on the solutions from the subproblems. x = {27.601470509, 0.398529491}

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