x^2+13x-36=0

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Solution for x^2+13x-36=0 equation:


Simplifying
x2 + 13x + -36 = 0

Reorder the terms:
-36 + 13x + x2 = 0

Solving
-36 + 13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 13x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + 13x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 13x + x2 = 0 + 36
13x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
13x + x2 = 36

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 = 36 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 36 + 42.25

Combine like terms: 36 + 42.25 = 78.25
42.25 + 13x + x2 = 78.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 78.25

Calculate the square root of the right side: 8.845903006

Break this problem into two subproblems by setting 
(x + 6.5) equal to 8.845903006 and -8.845903006.

Subproblem 1

x + 6.5 = 8.845903006 Simplifying x + 6.5 = 8.845903006 Reorder the terms: 6.5 + x = 8.845903006 Solving 6.5 + x = 8.845903006 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 = 8.845903006 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 8.845903006 + -6.5 x = 8.845903006 + -6.5 Combine like terms: 8.845903006 + -6.5 = 2.345903006 x = 2.345903006 Simplifying x = 2.345903006

Subproblem 2

x + 6.5 = -8.845903006 Simplifying x + 6.5 = -8.845903006 Reorder the terms: 6.5 + x = -8.845903006 Solving 6.5 + x = -8.845903006 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 = -8.845903006 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -8.845903006 + -6.5 x = -8.845903006 + -6.5 Combine like terms: -8.845903006 + -6.5 = -15.345903006 x = -15.345903006 Simplifying x = -15.345903006

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.345903006, -15.345903006}

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