18x^2-97x-136=0

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Solution for 18x^2-97x-136=0 equation: 


Simplifying
18x2 + -97x + -136 = 0

Reorder the terms:
-136 + -97x + 18x2 = 0

Solving
-136 + -97x + 18x2 = 0

Solving for variable 'x'.

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

Divide each side by '18'.
-7.555555556 + -5.388888889x + x2 = 0

Move the constant term to the right:

Add '7.555555556' to each side of the equation.
-7.555555556 + -5.388888889x + 7.555555556 + x2 = 0 + 7.555555556

Reorder the terms:
-7.555555556 + 7.555555556 + -5.388888889x + x2 = 0 + 7.555555556

Combine like terms: -7.555555556 + 7.555555556 = 0.000000000
0.000000000 + -5.388888889x + x2 = 0 + 7.555555556
-5.388888889x + x2 = 0 + 7.555555556

Combine like terms: 0 + 7.555555556 = 7.555555556
-5.388888889x + x2 = 7.555555556

The x term is -5.388888889x.  Take half its coefficient (-2.694444445).
Square it (7.260030867) and add it to both sides.

Add '7.260030867' to each side of the equation.
-5.388888889x + 7.260030867 + x2 = 7.555555556 + 7.260030867

Reorder the terms:
7.260030867 + -5.388888889x + x2 = 7.555555556 + 7.260030867

Combine like terms: 7.555555556 + 7.260030867 = 14.815586423
7.260030867 + -5.388888889x + x2 = 14.815586423

Factor a perfect square on the left side:
(x + -2.694444445)(x + -2.694444445) = 14.815586423

Calculate the square root of the right side: 3.849102028

Break this problem into two subproblems by setting 
(x + -2.694444445) equal to 3.849102028 and -3.849102028.


Subproblem 1
x + -2.694444445 = 3.849102028

Simplifying
x + -2.694444445 = 3.849102028

Reorder the terms:
-2.694444445 + x = 3.849102028

Solving
-2.694444445 + x = 3.849102028

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.694444445' to each side of the equation.
-2.694444445 + 2.694444445 + x = 3.849102028 + 2.694444445

Combine like terms: -2.694444445 + 2.694444445 = 0.000000000
0.000000000 + x = 3.849102028 + 2.694444445
x = 3.849102028 + 2.694444445

Combine like terms: 3.849102028 + 2.694444445 = 6.543546473
x = 6.543546473

Simplifying
x = 6.543546473


Subproblem 2
x + -2.694444445 = -3.849102028

Simplifying
x + -2.694444445 = -3.849102028

Reorder the terms:
-2.694444445 + x = -3.849102028

Solving
-2.694444445 + x = -3.849102028

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.694444445' to each side of the equation.
-2.694444445 + 2.694444445 + x = -3.849102028 + 2.694444445

Combine like terms: -2.694444445 + 2.694444445 = 0.000000000
0.000000000 + x = -3.849102028 + 2.694444445
x = -3.849102028 + 2.694444445

Combine like terms: -3.849102028 + 2.694444445 = -1.154657583
x = -1.154657583

Simplifying
x = -1.154657583


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.543546473, -1.154657583}

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