x^2-12x+29=0

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Solution for x^2-12x+29=0 equation:


Simplifying
x2 + -12x + 29 = 0

Reorder the terms:
29 + -12x + x2 = 0

Solving
29 + -12x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-29' to each side of the equation.
29 + -12x + -29 + x2 = 0 + -29

Reorder the terms:
29 + -29 + -12x + x2 = 0 + -29

Combine like terms: 29 + -29 = 0
0 + -12x + x2 = 0 + -29
-12x + x2 = 0 + -29

Combine like terms: 0 + -29 = -29
-12x + x2 = -29

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 = -29 + 36

Reorder the terms:
36 + -12x + x2 = -29 + 36

Combine like terms: -29 + 36 = 7
36 + -12x + x2 = 7

Factor a perfect square on the left side:
(x + -6)(x + -6) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + -6) equal to 2.645751311 and -2.645751311.

Subproblem 1

x + -6 = 2.645751311 Simplifying x + -6 = 2.645751311 Reorder the terms: -6 + x = 2.645751311 Solving -6 + x = 2.645751311 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 = 2.645751311 + 6 Combine like terms: -6 + 6 = 0 0 + x = 2.645751311 + 6 x = 2.645751311 + 6 Combine like terms: 2.645751311 + 6 = 8.645751311 x = 8.645751311 Simplifying x = 8.645751311

Subproblem 2

x + -6 = -2.645751311 Simplifying x + -6 = -2.645751311 Reorder the terms: -6 + x = -2.645751311 Solving -6 + x = -2.645751311 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 = -2.645751311 + 6 Combine like terms: -6 + 6 = 0 0 + x = -2.645751311 + 6 x = -2.645751311 + 6 Combine like terms: -2.645751311 + 6 = 3.354248689 x = 3.354248689 Simplifying x = 3.354248689

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.645751311, 3.354248689}

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