x^2+9x-111=0

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Solution for x^2+9x-111=0 equation:


Simplifying
x2 + 9x + -111 = 0

Reorder the terms:
-111 + 9x + x2 = 0

Solving
-111 + 9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '111' to each side of the equation.
-111 + 9x + 111 + x2 = 0 + 111

Reorder the terms:
-111 + 111 + 9x + x2 = 0 + 111

Combine like terms: -111 + 111 = 0
0 + 9x + x2 = 0 + 111
9x + x2 = 0 + 111

Combine like terms: 0 + 111 = 111
9x + x2 = 111

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 = 111 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 111 + 20.25

Combine like terms: 111 + 20.25 = 131.25
20.25 + 9x + x2 = 131.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 131.25

Calculate the square root of the right side: 11.456439237

Break this problem into two subproblems by setting 
(x + 4.5) equal to 11.456439237 and -11.456439237.

Subproblem 1

x + 4.5 = 11.456439237 Simplifying x + 4.5 = 11.456439237 Reorder the terms: 4.5 + x = 11.456439237 Solving 4.5 + x = 11.456439237 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 = 11.456439237 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 11.456439237 + -4.5 x = 11.456439237 + -4.5 Combine like terms: 11.456439237 + -4.5 = 6.956439237 x = 6.956439237 Simplifying x = 6.956439237

Subproblem 2

x + 4.5 = -11.456439237 Simplifying x + 4.5 = -11.456439237 Reorder the terms: 4.5 + x = -11.456439237 Solving 4.5 + x = -11.456439237 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 = -11.456439237 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -11.456439237 + -4.5 x = -11.456439237 + -4.5 Combine like terms: -11.456439237 + -4.5 = -15.956439237 x = -15.956439237 Simplifying x = -15.956439237

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.956439237, -15.956439237}

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