(9x^2)-18x+9=47

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Solution for (9x^2)-18x+9=47 equation:


Simplifying
(9x2) + -18x + 9 = 47

Reorder the terms:
9 + -18x + (9x2) = 47

Solving
9 + -18x + (9x2) = 47

Solving for variable 'x'.

Reorder the terms:
9 + -47 + -18x + (9x2) = 47 + -47

Combine like terms: 9 + -47 = -38
-38 + -18x + (9x2) = 47 + -47

Combine like terms: 47 + -47 = 0
-38 + -18x + (9x2) = 0

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

Divide each side by '9'.
-4.222222222 + -2x + x2 = 0

Move the constant term to the right:

Add '4.222222222' to each side of the equation.
-4.222222222 + -2x + 4.222222222 + x2 = 0 + 4.222222222

Reorder the terms:
-4.222222222 + 4.222222222 + -2x + x2 = 0 + 4.222222222

Combine like terms: -4.222222222 + 4.222222222 = 0.000000000
0.000000000 + -2x + x2 = 0 + 4.222222222
-2x + x2 = 0 + 4.222222222

Combine like terms: 0 + 4.222222222 = 4.222222222
-2x + x2 = 4.222222222

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 4.222222222 + 1

Reorder the terms:
1 + -2x + x2 = 4.222222222 + 1

Combine like terms: 4.222222222 + 1 = 5.222222222
1 + -2x + x2 = 5.222222222

Factor a perfect square on the left side:
((x) + -1)((x) + -1) = 5.222222222

Calculate the square root of the right side: 2.2852182

Break this problem into two subproblems by setting 
((x) + -1) equal to 2.2852182 and -2.2852182.

Subproblem 1

(x) + -1 = 2.2852182 Simplifying (x) + -1 = 2.2852182 x + -1 = 2.2852182 Reorder the terms: -1 + x = 2.2852182 Solving -1 + x = 2.2852182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.2852182 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.2852182 + 1 x = 2.2852182 + 1 Combine like terms: 2.2852182 + 1 = 3.2852182 x = 3.2852182 Simplifying x = 3.2852182

Subproblem 2

(x) + -1 = -2.2852182 Simplifying (x) + -1 = -2.2852182 x + -1 = -2.2852182 Reorder the terms: -1 + x = -2.2852182 Solving -1 + x = -2.2852182 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.2852182 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.2852182 + 1 x = -2.2852182 + 1 Combine like terms: -2.2852182 + 1 = -1.2852182 x = -1.2852182 Simplifying x = -1.2852182

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.2852182, -1.2852182}

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