9x^2-x-2=0

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


Simplifying
9x2 + -1x + -2 = 0

Reorder the terms:
-2 + -1x + 9x2 = 0

Solving
-2 + -1x + 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'.
-0.2222222222 + -0.1111111111x + x2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + -0.1111111111x + 0.2222222222 + x2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + -0.1111111111x + x2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + -0.1111111111x + x2 = 0 + 0.2222222222
-0.1111111111x + x2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
-0.1111111111x + x2 = 0.2222222222

The x term is -0.1111111111x.  Take half its coefficient (-0.05555555555).
Square it (0.003086419752) and add it to both sides.

Add '0.003086419752' to each side of the equation.
-0.1111111111x + 0.003086419752 + x2 = 0.2222222222 + 0.003086419752

Reorder the terms:
0.003086419752 + -0.1111111111x + x2 = 0.2222222222 + 0.003086419752

Combine like terms: 0.2222222222 + 0.003086419752 = 0.225308641952
0.003086419752 + -0.1111111111x + x2 = 0.225308641952

Factor a perfect square on the left side:
(x + -0.05555555555)(x + -0.05555555555) = 0.225308641952

Calculate the square root of the right side: 0.474666875

Break this problem into two subproblems by setting 
(x + -0.05555555555) equal to 0.474666875 and -0.474666875.

Subproblem 1

x + -0.05555555555 = 0.474666875 Simplifying x + -0.05555555555 = 0.474666875 Reorder the terms: -0.05555555555 + x = 0.474666875 Solving -0.05555555555 + x = 0.474666875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + x = 0.474666875 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = 0.474666875 + 0.05555555555 x = 0.474666875 + 0.05555555555 Combine like terms: 0.474666875 + 0.05555555555 = 0.53022243055 x = 0.53022243055 Simplifying x = 0.53022243055

Subproblem 2

x + -0.05555555555 = -0.474666875 Simplifying x + -0.05555555555 = -0.474666875 Reorder the terms: -0.05555555555 + x = -0.474666875 Solving -0.05555555555 + x = -0.474666875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + x = -0.474666875 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = -0.474666875 + 0.05555555555 x = -0.474666875 + 0.05555555555 Combine like terms: -0.474666875 + 0.05555555555 = -0.41911131945 x = -0.41911131945 Simplifying x = -0.41911131945

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.53022243055, -0.41911131945}

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