184+16x=(5x)(x+1)

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Solution for 184+16x=(5x)(x+1) equation:


Simplifying
184 + 16x = (5x)(x + 1)

Remove parenthesis around (5x)
184 + 16x = 5x(x + 1)

Reorder the terms:
184 + 16x = 5x(1 + x)
184 + 16x = (1 * 5x + x * 5x)
184 + 16x = (5x + 5x2)

Solving
184 + 16x = 5x + 5x2

Solving for variable 'x'.

Combine like terms: 16x + -5x = 11x
184 + 11x + -5x2 = 5x + 5x2 + -5x + -5x2

Reorder the terms:
184 + 11x + -5x2 = 5x + -5x + 5x2 + -5x2

Combine like terms: 5x + -5x = 0
184 + 11x + -5x2 = 0 + 5x2 + -5x2
184 + 11x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
184 + 11x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-36.8 + -2.2x + x2 = 0

Move the constant term to the right:

Add '36.8' to each side of the equation.
-36.8 + -2.2x + 36.8 + x2 = 0 + 36.8

Reorder the terms:
-36.8 + 36.8 + -2.2x + x2 = 0 + 36.8

Combine like terms: -36.8 + 36.8 = 0.0
0.0 + -2.2x + x2 = 0 + 36.8
-2.2x + x2 = 0 + 36.8

Combine like terms: 0 + 36.8 = 36.8
-2.2x + x2 = 36.8

The x term is -2.2x.  Take half its coefficient (-1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
-2.2x + 1.21 + x2 = 36.8 + 1.21

Reorder the terms:
1.21 + -2.2x + x2 = 36.8 + 1.21

Combine like terms: 36.8 + 1.21 = 38.01
1.21 + -2.2x + x2 = 38.01

Factor a perfect square on the left side:
(x + -1.1)(x + -1.1) = 38.01

Calculate the square root of the right side: 6.165225057

Break this problem into two subproblems by setting 
(x + -1.1) equal to 6.165225057 and -6.165225057.

Subproblem 1

x + -1.1 = 6.165225057 Simplifying x + -1.1 = 6.165225057 Reorder the terms: -1.1 + x = 6.165225057 Solving -1.1 + x = 6.165225057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = 6.165225057 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 6.165225057 + 1.1 x = 6.165225057 + 1.1 Combine like terms: 6.165225057 + 1.1 = 7.265225057 x = 7.265225057 Simplifying x = 7.265225057

Subproblem 2

x + -1.1 = -6.165225057 Simplifying x + -1.1 = -6.165225057 Reorder the terms: -1.1 + x = -6.165225057 Solving -1.1 + x = -6.165225057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = -6.165225057 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -6.165225057 + 1.1 x = -6.165225057 + 1.1 Combine like terms: -6.165225057 + 1.1 = -5.065225057 x = -5.065225057 Simplifying x = -5.065225057

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.265225057, -5.065225057}

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