69-x=x^2+9

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Solution for 69-x=x^2+9 equation:


Simplifying
69 + -1x = x2 + 9

Reorder the terms:
69 + -1x = 9 + x2

Solving
69 + -1x = 9 + x2

Solving for variable 'x'.

Reorder the terms:
69 + -9 + -1x + -1x2 = 9 + x2 + -9 + -1x2

Combine like terms: 69 + -9 = 60
60 + -1x + -1x2 = 9 + x2 + -9 + -1x2

Reorder the terms:
60 + -1x + -1x2 = 9 + -9 + x2 + -1x2

Combine like terms: 9 + -9 = 0
60 + -1x + -1x2 = 0 + x2 + -1x2
60 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
60 + -1x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-60 + x + x2 = 0

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + x + x2 = 0 + 60
x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
x + x2 = 60

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 60 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 60 + 0.25

Combine like terms: 60 + 0.25 = 60.25
1.25 + x2 = 60.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 60.25

Calculate the square root of the right side: 7.762087348

Break this problem into two subproblems by setting 
(x + 0.5) equal to 7.762087348 and -7.762087348.

Subproblem 1

x + 0.5 = 7.762087348 Simplifying x + 0.5 = 7.762087348 Reorder the terms: 0.5 + x = 7.762087348 Solving 0.5 + x = 7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 7.762087348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.762087348 + -0.5 x = 7.762087348 + -0.5 Combine like terms: 7.762087348 + -0.5 = 7.262087348 x = 7.262087348 Simplifying x = 7.262087348

Subproblem 2

x + 0.5 = -7.762087348 Simplifying x + 0.5 = -7.762087348 Reorder the terms: 0.5 + x = -7.762087348 Solving 0.5 + x = -7.762087348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -7.762087348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.762087348 + -0.5 x = -7.762087348 + -0.5 Combine like terms: -7.762087348 + -0.5 = -8.262087348 x = -8.262087348 Simplifying x = -8.262087348

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.262087348, -8.262087348}

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