x^2+19=12x

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Solution for x^2+19=12x equation:


Simplifying
x2 + 19 = 12x

Reorder the terms:
19 + x2 = 12x

Solving
19 + x2 = 12x

Solving for variable 'x'.

Reorder the terms:
19 + -12x + x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
19 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + -12x + -19 + x2 = 0 + -19

Reorder the terms:
19 + -19 + -12x + x2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -12x + x2 = 0 + -19
-12x + x2 = 0 + -19

Combine like terms: 0 + -19 = -19
-12x + x2 = -19

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 = -19 + 36

Reorder the terms:
36 + -12x + x2 = -19 + 36

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

Factor a perfect square on the left side:
(x + -6)(x + -6) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(x + -6) equal to 4.123105626 and -4.123105626.

Subproblem 1

x + -6 = 4.123105626 Simplifying x + -6 = 4.123105626 Reorder the terms: -6 + x = 4.123105626 Solving -6 + x = 4.123105626 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 = 4.123105626 + 6 Combine like terms: -6 + 6 = 0 0 + x = 4.123105626 + 6 x = 4.123105626 + 6 Combine like terms: 4.123105626 + 6 = 10.123105626 x = 10.123105626 Simplifying x = 10.123105626

Subproblem 2

x + -6 = -4.123105626 Simplifying x + -6 = -4.123105626 Reorder the terms: -6 + x = -4.123105626 Solving -6 + x = -4.123105626 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 = -4.123105626 + 6 Combine like terms: -6 + 6 = 0 0 + x = -4.123105626 + 6 x = -4.123105626 + 6 Combine like terms: -4.123105626 + 6 = 1.876894374 x = 1.876894374 Simplifying x = 1.876894374

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.123105626, 1.876894374}

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