2x^2-11x-18=0

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Solution for 2x^2-11x-18=0 equation:


Simplifying
2x2 + -11x + -18 = 0

Reorder the terms:
-18 + -11x + 2x2 = 0

Solving
-18 + -11x + 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'.
-9 + -5.5x + x2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -5.5x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -5.5x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -5.5x + x2 = 0 + 9
-5.5x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-5.5x + x2 = 9

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = 9 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 9 + 7.5625

Combine like terms: 9 + 7.5625 = 16.5625
7.5625 + -5.5x + x2 = 16.5625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 16.5625

Calculate the square root of the right side: 4.069705149

Break this problem into two subproblems by setting 
(x + -2.75) equal to 4.069705149 and -4.069705149.

Subproblem 1

x + -2.75 = 4.069705149 Simplifying x + -2.75 = 4.069705149 Reorder the terms: -2.75 + x = 4.069705149 Solving -2.75 + x = 4.069705149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 4.069705149 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 4.069705149 + 2.75 x = 4.069705149 + 2.75 Combine like terms: 4.069705149 + 2.75 = 6.819705149 x = 6.819705149 Simplifying x = 6.819705149

Subproblem 2

x + -2.75 = -4.069705149 Simplifying x + -2.75 = -4.069705149 Reorder the terms: -2.75 + x = -4.069705149 Solving -2.75 + x = -4.069705149 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -4.069705149 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -4.069705149 + 2.75 x = -4.069705149 + 2.75 Combine like terms: -4.069705149 + 2.75 = -1.319705149 x = -1.319705149 Simplifying x = -1.319705149

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.819705149, -1.319705149}

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