18x=3x^2+5

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


Simplifying
18x = 3x2 + 5

Reorder the terms:
18x = 5 + 3x2

Solving
18x = 5 + 3x2

Solving for variable 'x'.

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

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

Combine like terms: 5 + -5 = 0
-5 + 18x + -3x2 = 0 + 3x2 + -3x2
-5 + 18x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-5 + 18x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
1.666666667 + -6x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -6x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -6x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -6x + x2 = 0 + -1.666666667
-6x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-6x + x2 = -1.666666667

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 = -1.666666667 + 9

Reorder the terms:
9 + -6x + x2 = -1.666666667 + 9

Combine like terms: -1.666666667 + 9 = 7.333333333
9 + -6x + x2 = 7.333333333

Factor a perfect square on the left side:
(x + -3)(x + -3) = 7.333333333

Calculate the square root of the right side: 2.708012801

Break this problem into two subproblems by setting 
(x + -3) equal to 2.708012801 and -2.708012801.


Subproblem 1
x + -3 = 2.708012801

Simplifying
x + -3 = 2.708012801

Reorder the terms:
-3 + x = 2.708012801

Solving
-3 + x = 2.708012801

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 = 2.708012801 + 3

Combine like terms: -3 + 3 = 0
0 + x = 2.708012801 + 3
x = 2.708012801 + 3

Combine like terms: 2.708012801 + 3 = 5.708012801
x = 5.708012801

Simplifying
x = 5.708012801


Subproblem 2
x + -3 = -2.708012801

Simplifying
x + -3 = -2.708012801

Reorder the terms:
-3 + x = -2.708012801

Solving
-3 + x = -2.708012801

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 = -2.708012801 + 3

Combine like terms: -3 + 3 = 0
0 + x = -2.708012801 + 3
x = -2.708012801 + 3

Combine like terms: -2.708012801 + 3 = 0.291987199
x = 0.291987199

Simplifying
x = 0.291987199


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.708012801, 0.291987199}

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