12x=18-x^2

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Solution for 12x=18-x^2 equation:


Simplifying
12x = 18 + -1x2

Solving
12x = 18 + -1x2

Solving for variable 'x'.

Reorder the terms:
-18 + 12x + x2 = 18 + -1x2 + -18 + x2

Reorder the terms:
-18 + 12x + x2 = 18 + -18 + -1x2 + x2

Combine like terms: 18 + -18 = 0
-18 + 12x + x2 = 0 + -1x2 + x2
-18 + 12x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-18 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 12x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + 12x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 12x + x2 = 0 + 18
12x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
12x + x2 = 18

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 18 + 36

Reorder the terms:
36 + 12x + x2 = 18 + 36

Combine like terms: 18 + 36 = 54
36 + 12x + x2 = 54

Factor a perfect square on the left side:
(x + 6)(x + 6) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(x + 6) equal to 7.348469228 and -7.348469228.

Subproblem 1

x + 6 = 7.348469228 Simplifying x + 6 = 7.348469228 Reorder the terms: 6 + x = 7.348469228 Solving 6 + x = 7.348469228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 7.348469228 + -6 Combine like terms: 6 + -6 = 0 0 + x = 7.348469228 + -6 x = 7.348469228 + -6 Combine like terms: 7.348469228 + -6 = 1.348469228 x = 1.348469228 Simplifying x = 1.348469228

Subproblem 2

x + 6 = -7.348469228 Simplifying x + 6 = -7.348469228 Reorder the terms: 6 + x = -7.348469228 Solving 6 + x = -7.348469228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -7.348469228 + -6 Combine like terms: 6 + -6 = 0 0 + x = -7.348469228 + -6 x = -7.348469228 + -6 Combine like terms: -7.348469228 + -6 = -13.348469228 x = -13.348469228 Simplifying x = -13.348469228

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.348469228, -13.348469228}

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