2x^2+17x+18=0

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Solution for 2x^2+17x+18=0 equation:


Simplifying
2x2 + 17x + 18 = 0

Reorder the terms:
18 + 17x + 2x2 = 0

Solving
18 + 17x + 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 + 8.5x + x2 = 0

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + 8.5x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + 8.5x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 8.5x + x2 = 0 + -9
8.5x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
8.5x + x2 = -9

The x term is 8.5x.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5x + 18.0625 + x2 = -9 + 18.0625

Reorder the terms:
18.0625 + 8.5x + x2 = -9 + 18.0625

Combine like terms: -9 + 18.0625 = 9.0625
18.0625 + 8.5x + x2 = 9.0625

Factor a perfect square on the left side:
(x + 4.25)(x + 4.25) = 9.0625

Calculate the square root of the right side: 3.010398645

Break this problem into two subproblems by setting 
(x + 4.25) equal to 3.010398645 and -3.010398645.

Subproblem 1

x + 4.25 = 3.010398645 Simplifying x + 4.25 = 3.010398645 Reorder the terms: 4.25 + x = 3.010398645 Solving 4.25 + x = 3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 3.010398645 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 3.010398645 + -4.25 x = 3.010398645 + -4.25 Combine like terms: 3.010398645 + -4.25 = -1.239601355 x = -1.239601355 Simplifying x = -1.239601355

Subproblem 2

x + 4.25 = -3.010398645 Simplifying x + 4.25 = -3.010398645 Reorder the terms: 4.25 + x = -3.010398645 Solving 4.25 + x = -3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -3.010398645 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -3.010398645 + -4.25 x = -3.010398645 + -4.25 Combine like terms: -3.010398645 + -4.25 = -7.260398645 x = -7.260398645 Simplifying x = -7.260398645

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.239601355, -7.260398645}

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