=9x^2+2x-3

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Solution for =9x^2+2x-3 equation:


Simplifying
0 = 9x2 + 2x + -3

Reorder the terms:
0 = -3 + 2x + 9x2

Solving
0 = -3 + 2x + 9x2

Solving for variable 'x'.

Combine like terms: 0 + 3 = 3
3 + -2x + -9x2 = -3 + 2x + 9x2 + 3 + -2x + -9x2

Reorder the terms:
3 + -2x + -9x2 = -3 + 3 + 2x + -2x + 9x2 + -9x2

Combine like terms: -3 + 3 = 0
3 + -2x + -9x2 = 0 + 2x + -2x + 9x2 + -9x2
3 + -2x + -9x2 = 2x + -2x + 9x2 + -9x2

Combine like terms: 2x + -2x = 0
3 + -2x + -9x2 = 0 + 9x2 + -9x2
3 + -2x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
3 + -2x + -9x2 = 0

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

Divide each side by '-9'.
-0.3333333333 + 0.2222222222x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 0.2222222222x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 0.2222222222x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.2222222222x + x2 = 0 + 0.3333333333
0.2222222222x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
0.2222222222x + x2 = 0.3333333333

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 = 0.3333333333 + 0.01234567901

Reorder the terms:
0.01234567901 + 0.2222222222x + x2 = 0.3333333333 + 0.01234567901

Combine like terms: 0.3333333333 + 0.01234567901 = 0.34567901231
0.01234567901 + 0.2222222222x + x2 = 0.34567901231

Factor a perfect square on the left side:
(x + 0.1111111111)(x + 0.1111111111) = 0.34567901231

Calculate the square root of the right side: 0.587944736

Break this problem into two subproblems by setting 
(x + 0.1111111111) equal to 0.587944736 and -0.587944736.

Subproblem 1

x + 0.1111111111 = 0.587944736 Simplifying x + 0.1111111111 = 0.587944736 Reorder the terms: 0.1111111111 + x = 0.587944736 Solving 0.1111111111 + x = 0.587944736 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 = 0.587944736 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 0.587944736 + -0.1111111111 x = 0.587944736 + -0.1111111111 Combine like terms: 0.587944736 + -0.1111111111 = 0.4768336249 x = 0.4768336249 Simplifying x = 0.4768336249

Subproblem 2

x + 0.1111111111 = -0.587944736 Simplifying x + 0.1111111111 = -0.587944736 Reorder the terms: 0.1111111111 + x = -0.587944736 Solving 0.1111111111 + x = -0.587944736 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 = -0.587944736 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -0.587944736 + -0.1111111111 x = -0.587944736 + -0.1111111111 Combine like terms: -0.587944736 + -0.1111111111 = -0.6990558471 x = -0.6990558471 Simplifying x = -0.6990558471

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.4768336249, -0.6990558471}

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