2x^2-9x-2=0

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


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

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

Solving
-2 + -9x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-1 + -4.5x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -4.5x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -4.5x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4.5x + x2 = 0 + 1
-4.5x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-4.5x + x2 = 1

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 1 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 1 + 5.0625

Combine like terms: 1 + 5.0625 = 6.0625
5.0625 + -4.5x + x2 = 6.0625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 6.0625

Calculate the square root of the right side: 2.46221445

Break this problem into two subproblems by setting 
(x + -2.25) equal to 2.46221445 and -2.46221445.

Subproblem 1

x + -2.25 = 2.46221445 Simplifying x + -2.25 = 2.46221445 Reorder the terms: -2.25 + x = 2.46221445 Solving -2.25 + x = 2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 2.46221445 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 2.46221445 + 2.25 x = 2.46221445 + 2.25 Combine like terms: 2.46221445 + 2.25 = 4.71221445 x = 4.71221445 Simplifying x = 4.71221445

Subproblem 2

x + -2.25 = -2.46221445 Simplifying x + -2.25 = -2.46221445 Reorder the terms: -2.25 + x = -2.46221445 Solving -2.25 + x = -2.46221445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -2.46221445 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -2.46221445 + 2.25 x = -2.46221445 + 2.25 Combine like terms: -2.46221445 + 2.25 = -0.21221445 x = -0.21221445 Simplifying x = -0.21221445

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.71221445, -0.21221445}

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