x^2+9x-3240=0

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Solution for x^2+9x-3240=0 equation:


Simplifying
x2 + 9x + -3240 = 0

Reorder the terms:
-3240 + 9x + x2 = 0

Solving
-3240 + 9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '3240' to each side of the equation.
-3240 + 9x + 3240 + x2 = 0 + 3240

Reorder the terms:
-3240 + 3240 + 9x + x2 = 0 + 3240

Combine like terms: -3240 + 3240 = 0
0 + 9x + x2 = 0 + 3240
9x + x2 = 0 + 3240

Combine like terms: 0 + 3240 = 3240
9x + x2 = 3240

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 = 3240 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 3240 + 20.25

Combine like terms: 3240 + 20.25 = 3260.25
20.25 + 9x + x2 = 3260.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 3260.25

Calculate the square root of the right side: 57.098598932

Break this problem into two subproblems by setting 
(x + 4.5) equal to 57.098598932 and -57.098598932.

Subproblem 1

x + 4.5 = 57.098598932 Simplifying x + 4.5 = 57.098598932 Reorder the terms: 4.5 + x = 57.098598932 Solving 4.5 + x = 57.098598932 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 = 57.098598932 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 57.098598932 + -4.5 x = 57.098598932 + -4.5 Combine like terms: 57.098598932 + -4.5 = 52.598598932 x = 52.598598932 Simplifying x = 52.598598932

Subproblem 2

x + 4.5 = -57.098598932 Simplifying x + 4.5 = -57.098598932 Reorder the terms: 4.5 + x = -57.098598932 Solving 4.5 + x = -57.098598932 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 = -57.098598932 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -57.098598932 + -4.5 x = -57.098598932 + -4.5 Combine like terms: -57.098598932 + -4.5 = -61.598598932 x = -61.598598932 Simplifying x = -61.598598932

Solution

The solution to the problem is based on the solutions from the subproblems. x = {52.598598932, -61.598598932}

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