3x^2-18x+5=47

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Solution for 3x^2-18x+5=47 equation: 


Simplifying
3x2 + -18x + 5 = 47

Reorder the terms:
5 + -18x + 3x2 = 47

Solving
5 + -18x + 3x2 = 47

Solving for variable 'x'.

Reorder the terms:
5 + -47 + -18x + 3x2 = 47 + -47

Combine like terms: 5 + -47 = -42
-42 + -18x + 3x2 = 47 + -47

Combine like terms: 47 + -47 = 0
-42 + -18x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + -6x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-14 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
-14 + -6x + x2 = 0

Solving
-14 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -6x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + -6x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -6x + x2 = 0 + 14
-6x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
-6x + x2 = 14

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 14 + 9

Reorder the terms:
9 + -6x + x2 = 14 + 9

Combine like terms: 14 + 9 = 23
9 + -6x + x2 = 23

Factor a perfect square on the left side:
(x + -3)(x + -3) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(x + -3) equal to 4.795831523 and -4.795831523.


Subproblem 1
x + -3 = 4.795831523

Simplifying
x + -3 = 4.795831523

Reorder the terms:
-3 + x = 4.795831523

Solving
-3 + x = 4.795831523

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 4.795831523 + 3

Combine like terms: -3 + 3 = 0
0 + x = 4.795831523 + 3
x = 4.795831523 + 3

Combine like terms: 4.795831523 + 3 = 7.795831523
x = 7.795831523

Simplifying
x = 7.795831523


Subproblem 2
x + -3 = -4.795831523

Simplifying
x + -3 = -4.795831523

Reorder the terms:
-3 + x = -4.795831523

Solving
-3 + x = -4.795831523

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -4.795831523 + 3

Combine like terms: -3 + 3 = 0
0 + x = -4.795831523 + 3
x = -4.795831523 + 3

Combine like terms: -4.795831523 + 3 = -1.795831523
x = -1.795831523

Simplifying
x = -1.795831523


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.795831523, -1.795831523}
Solution
x = {7.795831523, -1.795831523}

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