x^2+13x=180

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


Simplifying
x2 + 13x = 180

Reorder the terms:
13x + x2 = 180

Solving
13x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 13x + x2 = 180 + -180

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

Begin completing the square.

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + 13x + 180 + x2 = 0 + 180

Reorder the terms:
-180 + 180 + 13x + x2 = 0 + 180

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

Combine like terms: 0 + 180 = 180
13x + x2 = 180

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = 180 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 180 + 42.25

Combine like terms: 180 + 42.25 = 222.25
42.25 + 13x + x2 = 222.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 222.25

Calculate the square root of the right side: 14.908051516

Break this problem into two subproblems by setting 
(x + 6.5) equal to 14.908051516 and -14.908051516.

Subproblem 1

x + 6.5 = 14.908051516 Simplifying x + 6.5 = 14.908051516 Reorder the terms: 6.5 + x = 14.908051516 Solving 6.5 + x = 14.908051516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 14.908051516 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 14.908051516 + -6.5 x = 14.908051516 + -6.5 Combine like terms: 14.908051516 + -6.5 = 8.408051516 x = 8.408051516 Simplifying x = 8.408051516

Subproblem 2

x + 6.5 = -14.908051516 Simplifying x + 6.5 = -14.908051516 Reorder the terms: 6.5 + x = -14.908051516 Solving 6.5 + x = -14.908051516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -14.908051516 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -14.908051516 + -6.5 x = -14.908051516 + -6.5 Combine like terms: -14.908051516 + -6.5 = -21.408051516 x = -21.408051516 Simplifying x = -21.408051516

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.408051516, -21.408051516}

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