x(5x+13)=16

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Solution for x(5x+13)=16 equation:


Simplifying
x(5x + 13) = 16

Reorder the terms:
x(13 + 5x) = 16
(13 * x + 5x * x) = 16
(13x + 5x2) = 16

Solving
13x + 5x2 = 16

Solving for variable 'x'.

Reorder the terms:
-16 + 13x + 5x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 13x + 5x2 = 0

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

Divide each side by '5'.
-3.2 + 2.6x + x2 = 0

Move the constant term to the right:

Add '3.2' to each side of the equation.
-3.2 + 2.6x + 3.2 + x2 = 0 + 3.2

Reorder the terms:
-3.2 + 3.2 + 2.6x + x2 = 0 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + 2.6x + x2 = 0 + 3.2
2.6x + x2 = 0 + 3.2

Combine like terms: 0 + 3.2 = 3.2
2.6x + x2 = 3.2

The x term is 2.6x.  Take half its coefficient (1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
2.6x + 1.69 + x2 = 3.2 + 1.69

Reorder the terms:
1.69 + 2.6x + x2 = 3.2 + 1.69

Combine like terms: 3.2 + 1.69 = 4.89
1.69 + 2.6x + x2 = 4.89

Factor a perfect square on the left side:
(x + 1.3)(x + 1.3) = 4.89

Calculate the square root of the right side: 2.211334439

Break this problem into two subproblems by setting 
(x + 1.3) equal to 2.211334439 and -2.211334439.

Subproblem 1

x + 1.3 = 2.211334439 Simplifying x + 1.3 = 2.211334439 Reorder the terms: 1.3 + x = 2.211334439 Solving 1.3 + x = 2.211334439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = 2.211334439 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = 2.211334439 + -1.3 x = 2.211334439 + -1.3 Combine like terms: 2.211334439 + -1.3 = 0.911334439 x = 0.911334439 Simplifying x = 0.911334439

Subproblem 2

x + 1.3 = -2.211334439 Simplifying x + 1.3 = -2.211334439 Reorder the terms: 1.3 + x = -2.211334439 Solving 1.3 + x = -2.211334439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = -2.211334439 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = -2.211334439 + -1.3 x = -2.211334439 + -1.3 Combine like terms: -2.211334439 + -1.3 = -3.511334439 x = -3.511334439 Simplifying x = -3.511334439

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.911334439, -3.511334439}

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