x^2-16x+12=2

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Solution for x^2-16x+12=2 equation:


Simplifying
x2 + -16x + 12 = 2

Reorder the terms:
12 + -16x + x2 = 2

Solving
12 + -16x + x2 = 2

Solving for variable 'x'.

Reorder the terms:
12 + -2 + -16x + x2 = 2 + -2

Combine like terms: 12 + -2 = 10
10 + -16x + x2 = 2 + -2

Combine like terms: 2 + -2 = 0
10 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -16x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -16x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -16x + x2 = 0 + -10
-16x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-16x + x2 = -10

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = -10 + 64

Reorder the terms:
64 + -16x + x2 = -10 + 64

Combine like terms: -10 + 64 = 54
64 + -16x + x2 = 54

Factor a perfect square on the left side:
(x + -8)(x + -8) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(x + -8) equal to 7.348469228 and -7.348469228.

Subproblem 1

x + -8 = 7.348469228 Simplifying x + -8 = 7.348469228 Reorder the terms: -8 + x = 7.348469228 Solving -8 + x = 7.348469228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 7.348469228 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.348469228 + 8 x = 7.348469228 + 8 Combine like terms: 7.348469228 + 8 = 15.348469228 x = 15.348469228 Simplifying x = 15.348469228

Subproblem 2

x + -8 = -7.348469228 Simplifying x + -8 = -7.348469228 Reorder the terms: -8 + x = -7.348469228 Solving -8 + x = -7.348469228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -7.348469228 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.348469228 + 8 x = -7.348469228 + 8 Combine like terms: -7.348469228 + 8 = 0.651530772 x = 0.651530772 Simplifying x = 0.651530772

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.348469228, 0.651530772}

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