x^2+9x=13

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Solution for x^2+9x=13 equation:


Simplifying
x2 + 9x = 13

Reorder the terms:
9x + x2 = 13

Solving
9x + x2 = 13

Solving for variable 'x'.

Reorder the terms:
-13 + 9x + x2 = 13 + -13

Combine like terms: 13 + -13 = 0
-13 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + 9x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + 9x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 9x + x2 = 0 + 13
9x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
9x + x2 = 13

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 13 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 13 + 20.25

Combine like terms: 13 + 20.25 = 33.25
20.25 + 9x + x2 = 33.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 33.25

Calculate the square root of the right side: 5.766281297

Break this problem into two subproblems by setting 
(x + 4.5) equal to 5.766281297 and -5.766281297.

Subproblem 1

x + 4.5 = 5.766281297 Simplifying x + 4.5 = 5.766281297 Reorder the terms: 4.5 + x = 5.766281297 Solving 4.5 + x = 5.766281297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 5.766281297 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 5.766281297 + -4.5 x = 5.766281297 + -4.5 Combine like terms: 5.766281297 + -4.5 = 1.266281297 x = 1.266281297 Simplifying x = 1.266281297

Subproblem 2

x + 4.5 = -5.766281297 Simplifying x + 4.5 = -5.766281297 Reorder the terms: 4.5 + x = -5.766281297 Solving 4.5 + x = -5.766281297 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -5.766281297 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -5.766281297 + -4.5 x = -5.766281297 + -4.5 Combine like terms: -5.766281297 + -4.5 = -10.266281297 x = -10.266281297 Simplifying x = -10.266281297

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.266281297, -10.266281297}

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