9x^2-2x=2

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


Simplifying
9x2 + -2x = 2

Reorder the terms:
-2x + 9x2 = 2

Solving
-2x + 9x2 = 2

Solving for variable 'x'.

Reorder the terms:
-2 + -2x + 9x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -2x + 9x2 = 0

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

Divide each side by '9'.
-0.2222222222 + -0.2222222222x + x2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + -0.2222222222x + 0.2222222222 + x2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + -0.2222222222x + x2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + -0.2222222222x + x2 = 0 + 0.2222222222
-0.2222222222x + x2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
-0.2222222222x + x2 = 0.2222222222

The x term is -0.2222222222x.  Take half its coefficient (-0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
-0.2222222222x + 0.01234567901 + x2 = 0.2222222222 + 0.01234567901

Reorder the terms:
0.01234567901 + -0.2222222222x + x2 = 0.2222222222 + 0.01234567901

Combine like terms: 0.2222222222 + 0.01234567901 = 0.23456790121
0.01234567901 + -0.2222222222x + x2 = 0.23456790121

Factor a perfect square on the left side:
(x + -0.1111111111)(x + -0.1111111111) = 0.23456790121

Calculate the square root of the right side: 0.484322105

Break this problem into two subproblems by setting 
(x + -0.1111111111) equal to 0.484322105 and -0.484322105.

Subproblem 1

x + -0.1111111111 = 0.484322105 Simplifying x + -0.1111111111 = 0.484322105 Reorder the terms: -0.1111111111 + x = 0.484322105 Solving -0.1111111111 + x = 0.484322105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x = 0.484322105 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = 0.484322105 + 0.1111111111 x = 0.484322105 + 0.1111111111 Combine like terms: 0.484322105 + 0.1111111111 = 0.5954332161 x = 0.5954332161 Simplifying x = 0.5954332161

Subproblem 2

x + -0.1111111111 = -0.484322105 Simplifying x + -0.1111111111 = -0.484322105 Reorder the terms: -0.1111111111 + x = -0.484322105 Solving -0.1111111111 + x = -0.484322105 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1111111111' to each side of the equation. -0.1111111111 + 0.1111111111 + x = -0.484322105 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + x = -0.484322105 + 0.1111111111 x = -0.484322105 + 0.1111111111 Combine like terms: -0.484322105 + 0.1111111111 = -0.3732109939 x = -0.3732109939 Simplifying x = -0.3732109939

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.5954332161, -0.3732109939}

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