20-9x-x^2=12

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Solution for 20-9x-x^2=12 equation:


Simplifying
20 + -9x + -1x2 = 12

Solving
20 + -9x + -1x2 = 12

Solving for variable 'x'.

Reorder the terms:
20 + -12 + -9x + -1x2 = 12 + -12

Combine like terms: 20 + -12 = 8
8 + -9x + -1x2 = 12 + -12

Combine like terms: 12 + -12 = 0
8 + -9x + -1x2 = 0

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

Divide each side by '-1'.
-8 + 9x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 9x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 9x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 9x + x2 = 0 + 8
9x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
9x + x2 = 8

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 = 8 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 8 + 20.25

Combine like terms: 8 + 20.25 = 28.25
20.25 + 9x + x2 = 28.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 28.25

Calculate the square root of the right side: 5.315072906

Break this problem into two subproblems by setting 
(x + 4.5) equal to 5.315072906 and -5.315072906.

Subproblem 1

x + 4.5 = 5.315072906 Simplifying x + 4.5 = 5.315072906 Reorder the terms: 4.5 + x = 5.315072906 Solving 4.5 + x = 5.315072906 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 = 5.315072906 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 5.315072906 + -4.5 x = 5.315072906 + -4.5 Combine like terms: 5.315072906 + -4.5 = 0.815072906 x = 0.815072906 Simplifying x = 0.815072906

Subproblem 2

x + 4.5 = -5.315072906 Simplifying x + 4.5 = -5.315072906 Reorder the terms: 4.5 + x = -5.315072906 Solving 4.5 + x = -5.315072906 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 = -5.315072906 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -5.315072906 + -4.5 x = -5.315072906 + -4.5 Combine like terms: -5.315072906 + -4.5 = -9.815072906 x = -9.815072906 Simplifying x = -9.815072906

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.815072906, -9.815072906}

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