(2x^2)+13x=180

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Solution for (2x^2)+13x=180 equation:


Simplifying
(2x2) + 13x = 180

Reorder the terms:
13x + (2x2) = 180

Solving
13x + (2x2) = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 13x + (2x2) = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 13x + (2x2) = 0

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

Divide each side by '2'.
-90 + 6.5x + x2 = 0

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 6.5x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 6.5x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 6.5x + x2 = 0 + 90
6.5x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
6.5x + x2 = 90

The x term is 6.5x.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5x + 10.5625 + x2 = 90 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = 90 + 10.5625

Combine like terms: 90 + 10.5625 = 100.5625
10.5625 + 6.5x + x2 = 100.5625

Factor a perfect square on the left side:
((x) + 3.25)((x) + 3.25) = 100.5625

Calculate the square root of the right side: 10.02808556

Break this problem into two subproblems by setting 
((x) + 3.25) equal to 10.02808556 and -10.02808556.

Subproblem 1

(x) + 3.25 = 10.02808556 Simplifying (x) + 3.25 = 10.02808556 x + 3.25 = 10.02808556 Reorder the terms: 3.25 + x = 10.02808556 Solving 3.25 + x = 10.02808556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 10.02808556 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 10.02808556 + -3.25 x = 10.02808556 + -3.25 Combine like terms: 10.02808556 + -3.25 = 6.77808556 x = 6.77808556 Simplifying x = 6.77808556

Subproblem 2

(x) + 3.25 = -10.02808556 Simplifying (x) + 3.25 = -10.02808556 x + 3.25 = -10.02808556 Reorder the terms: 3.25 + x = -10.02808556 Solving 3.25 + x = -10.02808556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -10.02808556 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -10.02808556 + -3.25 x = -10.02808556 + -3.25 Combine like terms: -10.02808556 + -3.25 = -13.27808556 x = -13.27808556 Simplifying x = -13.27808556

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.77808556, -13.27808556}

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