9x=54-x^2

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Solution for 9x=54-x^2 equation:


Simplifying
9x = 54 + -1x2

Solving
9x = 54 + -1x2

Solving for variable 'x'.

Reorder the terms:
-54 + 9x + x2 = 54 + -1x2 + -54 + x2

Reorder the terms:
-54 + 9x + x2 = 54 + -54 + -1x2 + x2

Combine like terms: 54 + -54 = 0
-54 + 9x + x2 = 0 + -1x2 + x2
-54 + 9x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-54 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + 9x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + 9x + x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + 9x + x2 = 0 + 54
9x + x2 = 0 + 54

Combine like terms: 0 + 54 = 54
9x + x2 = 54

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 = 54 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 54 + 20.25

Combine like terms: 54 + 20.25 = 74.25
20.25 + 9x + x2 = 74.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 74.25

Calculate the square root of the right side: 8.61684397

Break this problem into two subproblems by setting 
(x + 4.5) equal to 8.61684397 and -8.61684397.

Subproblem 1

x + 4.5 = 8.61684397 Simplifying x + 4.5 = 8.61684397 Reorder the terms: 4.5 + x = 8.61684397 Solving 4.5 + x = 8.61684397 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 = 8.61684397 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 8.61684397 + -4.5 x = 8.61684397 + -4.5 Combine like terms: 8.61684397 + -4.5 = 4.11684397 x = 4.11684397 Simplifying x = 4.11684397

Subproblem 2

x + 4.5 = -8.61684397 Simplifying x + 4.5 = -8.61684397 Reorder the terms: 4.5 + x = -8.61684397 Solving 4.5 + x = -8.61684397 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 = -8.61684397 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -8.61684397 + -4.5 x = -8.61684397 + -4.5 Combine like terms: -8.61684397 + -4.5 = -13.11684397 x = -13.11684397 Simplifying x = -13.11684397

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.11684397, -13.11684397}

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