0=9x^2+2x-10

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Solution for 0=9x^2+2x-10 equation:


Simplifying
0 = 9x2 + 2x + -10

Reorder the terms:
0 = -10 + 2x + 9x2

Solving
0 = -10 + 2x + 9x2

Solving for variable 'x'.

Combine like terms: 0 + 10 = 10
10 + -2x + -9x2 = -10 + 2x + 9x2 + 10 + -2x + -9x2

Reorder the terms:
10 + -2x + -9x2 = -10 + 10 + 2x + -2x + 9x2 + -9x2

Combine like terms: -10 + 10 = 0
10 + -2x + -9x2 = 0 + 2x + -2x + 9x2 + -9x2
10 + -2x + -9x2 = 2x + -2x + 9x2 + -9x2

Combine like terms: 2x + -2x = 0
10 + -2x + -9x2 = 0 + 9x2 + -9x2
10 + -2x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
10 + -2x + -9x2 = 0

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

Divide each side by '-9'.
-1.111111111 + 0.2222222222x + x2 = 0

Move the constant term to the right:

Add '1.111111111' to each side of the equation.
-1.111111111 + 0.2222222222x + 1.111111111 + x2 = 0 + 1.111111111

Reorder the terms:
-1.111111111 + 1.111111111 + 0.2222222222x + x2 = 0 + 1.111111111

Combine like terms: -1.111111111 + 1.111111111 = 0.000000000
0.000000000 + 0.2222222222x + x2 = 0 + 1.111111111
0.2222222222x + x2 = 0 + 1.111111111

Combine like terms: 0 + 1.111111111 = 1.111111111
0.2222222222x + x2 = 1.111111111

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 = 1.111111111 + 0.01234567901

Reorder the terms:
0.01234567901 + 0.2222222222x + x2 = 1.111111111 + 0.01234567901

Combine like terms: 1.111111111 + 0.01234567901 = 1.12345679001
0.01234567901 + 0.2222222222x + x2 = 1.12345679001

Factor a perfect square on the left side:
(x + 0.1111111111)(x + 0.1111111111) = 1.12345679001

Calculate the square root of the right side: 1.059932446

Break this problem into two subproblems by setting 
(x + 0.1111111111) equal to 1.059932446 and -1.059932446.

Subproblem 1

x + 0.1111111111 = 1.059932446 Simplifying x + 0.1111111111 = 1.059932446 Reorder the terms: 0.1111111111 + x = 1.059932446 Solving 0.1111111111 + x = 1.059932446 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 = 1.059932446 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 1.059932446 + -0.1111111111 x = 1.059932446 + -0.1111111111 Combine like terms: 1.059932446 + -0.1111111111 = 0.9488213349 x = 0.9488213349 Simplifying x = 0.9488213349

Subproblem 2

x + 0.1111111111 = -1.059932446 Simplifying x + 0.1111111111 = -1.059932446 Reorder the terms: 0.1111111111 + x = -1.059932446 Solving 0.1111111111 + x = -1.059932446 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 = -1.059932446 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -1.059932446 + -0.1111111111 x = -1.059932446 + -0.1111111111 Combine like terms: -1.059932446 + -0.1111111111 = -1.1710435571 x = -1.1710435571 Simplifying x = -1.1710435571

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.9488213349, -1.1710435571}

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