x^2-12x+17=0

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Solution for x^2-12x+17=0 equation:


Simplifying
x2 + -12x + 17 = 0

Reorder the terms:
17 + -12x + x2 = 0

Solving
17 + -12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + -12x + -17 + x2 = 0 + -17

Reorder the terms:
17 + -17 + -12x + x2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -12x + x2 = 0 + -17
-12x + x2 = 0 + -17

Combine like terms: 0 + -17 = -17
-12x + x2 = -17

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -17 + 36

Reorder the terms:
36 + -12x + x2 = -17 + 36

Combine like terms: -17 + 36 = 19
36 + -12x + x2 = 19

Factor a perfect square on the left side:
(x + -6)(x + -6) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(x + -6) equal to 4.358898944 and -4.358898944.

Subproblem 1

x + -6 = 4.358898944 Simplifying x + -6 = 4.358898944 Reorder the terms: -6 + x = 4.358898944 Solving -6 + x = 4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 4.358898944 + 6 Combine like terms: -6 + 6 = 0 0 + x = 4.358898944 + 6 x = 4.358898944 + 6 Combine like terms: 4.358898944 + 6 = 10.358898944 x = 10.358898944 Simplifying x = 10.358898944

Subproblem 2

x + -6 = -4.358898944 Simplifying x + -6 = -4.358898944 Reorder the terms: -6 + x = -4.358898944 Solving -6 + x = -4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -4.358898944 + 6 Combine like terms: -6 + 6 = 0 0 + x = -4.358898944 + 6 x = -4.358898944 + 6 Combine like terms: -4.358898944 + 6 = 1.641101056 x = 1.641101056 Simplifying x = 1.641101056

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.358898944, 1.641101056}

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