x^2-4x+9=47

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Solution for x^2-4x+9=47 equation:


Simplifying
x2 + -4x + 9 = 47

Reorder the terms:
9 + -4x + x2 = 47

Solving
9 + -4x + x2 = 47

Solving for variable 'x'.

Reorder the terms:
9 + -47 + -4x + x2 = 47 + -47

Combine like terms: 9 + -47 = -38
-38 + -4x + x2 = 47 + -47

Combine like terms: 47 + -47 = 0
-38 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '38' to each side of the equation.
-38 + -4x + 38 + x2 = 0 + 38

Reorder the terms:
-38 + 38 + -4x + x2 = 0 + 38

Combine like terms: -38 + 38 = 0
0 + -4x + x2 = 0 + 38
-4x + x2 = 0 + 38

Combine like terms: 0 + 38 = 38
-4x + x2 = 38

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 38 + 4

Reorder the terms:
4 + -4x + x2 = 38 + 4

Combine like terms: 38 + 4 = 42
4 + -4x + x2 = 42

Factor a perfect square on the left side:
(x + -2)(x + -2) = 42

Calculate the square root of the right side: 6.480740698

Break this problem into two subproblems by setting 
(x + -2) equal to 6.480740698 and -6.480740698.


Subproblem 1
x + -2 = 6.480740698

Simplifying
x + -2 = 6.480740698

Reorder the terms:
-2 + x = 6.480740698

Solving
-2 + x = 6.480740698

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + x = 6.480740698 + 2

Combine like terms: -2 + 2 = 0
0 + x = 6.480740698 + 2
x = 6.480740698 + 2

Combine like terms: 6.480740698 + 2 = 8.480740698
x = 8.480740698

Simplifying
x = 8.480740698


Subproblem 2
x + -2 = -6.480740698

Simplifying
x + -2 = -6.480740698

Reorder the terms:
-2 + x = -6.480740698

Solving
-2 + x = -6.480740698

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + x = -6.480740698 + 2

Combine like terms: -2 + 2 = 0
0 + x = -6.480740698 + 2
x = -6.480740698 + 2

Combine like terms: -6.480740698 + 2 = -4.480740698
x = -4.480740698

Simplifying
x = -4.480740698


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.480740698, -4.480740698}

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