2x^2-13x-18=1

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Solution for 2x^2-13x-18=1 equation:


Simplifying
2x2 + -13x + -18 = 1

Reorder the terms:
-18 + -13x + 2x2 = 1

Solving
-18 + -13x + 2x2 = 1

Solving for variable 'x'.

Reorder the terms:
-18 + -1 + -13x + 2x2 = 1 + -1

Combine like terms: -18 + -1 = -19
-19 + -13x + 2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-19 + -13x + 2x2 = 0

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

Divide each side by '2'.
-9.5 + -6.5x + x2 = 0

Move the constant term to the right:

Add '9.5' to each side of the equation.
-9.5 + -6.5x + 9.5 + x2 = 0 + 9.5

Reorder the terms:
-9.5 + 9.5 + -6.5x + x2 = 0 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + -6.5x + x2 = 0 + 9.5
-6.5x + x2 = 0 + 9.5

Combine like terms: 0 + 9.5 = 9.5
-6.5x + x2 = 9.5

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = 9.5 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = 9.5 + 10.5625

Combine like terms: 9.5 + 10.5625 = 20.0625
10.5625 + -6.5x + x2 = 20.0625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 20.0625

Calculate the square root of the right side: 4.479118217

Break this problem into two subproblems by setting 
(x + -3.25) equal to 4.479118217 and -4.479118217.

Subproblem 1

x + -3.25 = 4.479118217 Simplifying x + -3.25 = 4.479118217 Reorder the terms: -3.25 + x = 4.479118217 Solving -3.25 + x = 4.479118217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 4.479118217 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 4.479118217 + 3.25 x = 4.479118217 + 3.25 Combine like terms: 4.479118217 + 3.25 = 7.729118217 x = 7.729118217 Simplifying x = 7.729118217

Subproblem 2

x + -3.25 = -4.479118217 Simplifying x + -3.25 = -4.479118217 Reorder the terms: -3.25 + x = -4.479118217 Solving -3.25 + x = -4.479118217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -4.479118217 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -4.479118217 + 3.25 x = -4.479118217 + 3.25 Combine like terms: -4.479118217 + 3.25 = -1.229118217 x = -1.229118217 Simplifying x = -1.229118217

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.729118217, -1.229118217}

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