3x^2+4x-16=45x

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Solution for 3x^2+4x-16=45x equation: 


Simplifying
3x2 + 4x + -16 = 45x

Reorder the terms:
-16 + 4x + 3x2 = 45x

Solving
-16 + 4x + 3x2 = 45x

Solving for variable 'x'.

Reorder the terms:
-16 + 4x + -45x + 3x2 = 45x + -45x

Combine like terms: 4x + -45x = -41x
-16 + -41x + 3x2 = 45x + -45x

Combine like terms: 45x + -45x = 0
-16 + -41x + 3x2 = 0

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

Divide each side by '3'.
-5.333333333 + -13.66666667x + x2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + -13.66666667x + 5.333333333 + x2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + -13.66666667x + x2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + -13.66666667x + x2 = 0 + 5.333333333
-13.66666667x + x2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
-13.66666667x + x2 = 5.333333333

The x term is -13.66666667x.  Take half its coefficient (-6.833333335).
Square it (46.69444447) and add it to both sides.

Add '46.69444447' to each side of the equation.
-13.66666667x + 46.69444447 + x2 = 5.333333333 + 46.69444447

Reorder the terms:
46.69444447 + -13.66666667x + x2 = 5.333333333 + 46.69444447

Combine like terms: 5.333333333 + 46.69444447 = 52.027777803
46.69444447 + -13.66666667x + x2 = 52.027777803

Factor a perfect square on the left side:
(x + -6.833333335)(x + -6.833333335) = 52.027777803

Calculate the square root of the right side: 7.213028338

Break this problem into two subproblems by setting 
(x + -6.833333335) equal to 7.213028338 and -7.213028338.


Subproblem 1
x + -6.833333335 = 7.213028338

Simplifying
x + -6.833333335 = 7.213028338

Reorder the terms:
-6.833333335 + x = 7.213028338

Solving
-6.833333335 + x = 7.213028338

Solving for variable 'x'.

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

Add '6.833333335' to each side of the equation.
-6.833333335 + 6.833333335 + x = 7.213028338 + 6.833333335

Combine like terms: -6.833333335 + 6.833333335 = 0.000000000
0.000000000 + x = 7.213028338 + 6.833333335
x = 7.213028338 + 6.833333335

Combine like terms: 7.213028338 + 6.833333335 = 14.046361673
x = 14.046361673

Simplifying
x = 14.046361673


Subproblem 2
x + -6.833333335 = -7.213028338

Simplifying
x + -6.833333335 = -7.213028338

Reorder the terms:
-6.833333335 + x = -7.213028338

Solving
-6.833333335 + x = -7.213028338

Solving for variable 'x'.

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

Add '6.833333335' to each side of the equation.
-6.833333335 + 6.833333335 + x = -7.213028338 + 6.833333335

Combine like terms: -6.833333335 + 6.833333335 = 0.000000000
0.000000000 + x = -7.213028338 + 6.833333335
x = -7.213028338 + 6.833333335

Combine like terms: -7.213028338 + 6.833333335 = -0.379695003
x = -0.379695003

Simplifying
x = -0.379695003


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.046361673, -0.379695003}

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