9x^2+2x-9=0

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Solution for 9x^2+2x-9=0 equation:


Simplifying
9x2 + 2x + -9 = 0

Reorder the terms:
-9 + 2x + 9x2 = 0

Solving
-9 + 2x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-1 + 0.2222222222x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.2222222222x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.2222222222x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.2222222222x + x2 = 0 + 1
0.2222222222x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.2222222222x + x2 = 1

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 = 1 + 0.01234567901

Reorder the terms:
0.01234567901 + 0.2222222222x + x2 = 1 + 0.01234567901

Combine like terms: 1 + 0.01234567901 = 1.01234567901
0.01234567901 + 0.2222222222x + x2 = 1.01234567901

Factor a perfect square on the left side:
(x + 0.1111111111)(x + 0.1111111111) = 1.01234567901

Calculate the square root of the right side: 1.006153904

Break this problem into two subproblems by setting 
(x + 0.1111111111) equal to 1.006153904 and -1.006153904.

Subproblem 1

x + 0.1111111111 = 1.006153904 Simplifying x + 0.1111111111 = 1.006153904 Reorder the terms: 0.1111111111 + x = 1.006153904 Solving 0.1111111111 + x = 1.006153904 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 = 1.006153904 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 1.006153904 + -0.1111111111 x = 1.006153904 + -0.1111111111 Combine like terms: 1.006153904 + -0.1111111111 = 0.8950427929 x = 0.8950427929 Simplifying x = 0.8950427929

Subproblem 2

x + 0.1111111111 = -1.006153904 Simplifying x + 0.1111111111 = -1.006153904 Reorder the terms: 0.1111111111 + x = -1.006153904 Solving 0.1111111111 + x = -1.006153904 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 = -1.006153904 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -1.006153904 + -0.1111111111 x = -1.006153904 + -0.1111111111 Combine like terms: -1.006153904 + -0.1111111111 = -1.1172650151 x = -1.1172650151 Simplifying x = -1.1172650151

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.8950427929, -1.1172650151}

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