x^2=81-9x

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Solution for x^2=81-9x equation:


Simplifying
x2 = 81 + -9x

Solving
x2 = 81 + -9x

Solving for variable 'x'.

Reorder the terms:
-81 + 9x + x2 = 81 + -9x + -81 + 9x

Reorder the terms:
-81 + 9x + x2 = 81 + -81 + -9x + 9x

Combine like terms: 81 + -81 = 0
-81 + 9x + x2 = 0 + -9x + 9x
-81 + 9x + x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
-81 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '81' to each side of the equation.
-81 + 9x + 81 + x2 = 0 + 81

Reorder the terms:
-81 + 81 + 9x + x2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + 9x + x2 = 0 + 81
9x + x2 = 0 + 81

Combine like terms: 0 + 81 = 81
9x + x2 = 81

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 = 81 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 81 + 20.25

Combine like terms: 81 + 20.25 = 101.25
20.25 + 9x + x2 = 101.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 101.25

Calculate the square root of the right side: 10.062305899

Break this problem into two subproblems by setting 
(x + 4.5) equal to 10.062305899 and -10.062305899.

Subproblem 1

x + 4.5 = 10.062305899 Simplifying x + 4.5 = 10.062305899 Reorder the terms: 4.5 + x = 10.062305899 Solving 4.5 + x = 10.062305899 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 = 10.062305899 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 10.062305899 + -4.5 x = 10.062305899 + -4.5 Combine like terms: 10.062305899 + -4.5 = 5.562305899 x = 5.562305899 Simplifying x = 5.562305899

Subproblem 2

x + 4.5 = -10.062305899 Simplifying x + 4.5 = -10.062305899 Reorder the terms: 4.5 + x = -10.062305899 Solving 4.5 + x = -10.062305899 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 = -10.062305899 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -10.062305899 + -4.5 x = -10.062305899 + -4.5 Combine like terms: -10.062305899 + -4.5 = -14.562305899 x = -14.562305899 Simplifying x = -14.562305899

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.562305899, -14.562305899}

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