x^2+9x-84=0

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Solution for x^2+9x-84=0 equation:


Simplifying
x2 + 9x + -84 = 0

Reorder the terms:
-84 + 9x + x2 = 0

Solving
-84 + 9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '84' to each side of the equation.
-84 + 9x + 84 + x2 = 0 + 84

Reorder the terms:
-84 + 84 + 9x + x2 = 0 + 84

Combine like terms: -84 + 84 = 0
0 + 9x + x2 = 0 + 84
9x + x2 = 0 + 84

Combine like terms: 0 + 84 = 84
9x + x2 = 84

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 = 84 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 84 + 20.25

Combine like terms: 84 + 20.25 = 104.25
20.25 + 9x + x2 = 104.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 104.25

Calculate the square root of the right side: 10.210288928

Break this problem into two subproblems by setting 
(x + 4.5) equal to 10.210288928 and -10.210288928.

Subproblem 1

x + 4.5 = 10.210288928 Simplifying x + 4.5 = 10.210288928 Reorder the terms: 4.5 + x = 10.210288928 Solving 4.5 + x = 10.210288928 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 = 10.210288928 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 10.210288928 + -4.5 x = 10.210288928 + -4.5 Combine like terms: 10.210288928 + -4.5 = 5.710288928 x = 5.710288928 Simplifying x = 5.710288928

Subproblem 2

x + 4.5 = -10.210288928 Simplifying x + 4.5 = -10.210288928 Reorder the terms: 4.5 + x = -10.210288928 Solving 4.5 + x = -10.210288928 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 = -10.210288928 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -10.210288928 + -4.5 x = -10.210288928 + -4.5 Combine like terms: -10.210288928 + -4.5 = -14.710288928 x = -14.710288928 Simplifying x = -14.710288928

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.710288928, -14.710288928}

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