2x^2-18x-40=1

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Solution for 2x^2-18x-40=1 equation:


Simplifying
2x2 + -18x + -40 = 1

Reorder the terms:
-40 + -18x + 2x2 = 1

Solving
-40 + -18x + 2x2 = 1

Solving for variable 'x'.

Reorder the terms:
-40 + -1 + -18x + 2x2 = 1 + -1

Combine like terms: -40 + -1 = -41
-41 + -18x + 2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-41 + -18x + 2x2 = 0

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

Divide each side by '2'.
-20.5 + -9x + x2 = 0

Move the constant term to the right:

Add '20.5' to each side of the equation.
-20.5 + -9x + 20.5 + x2 = 0 + 20.5

Reorder the terms:
-20.5 + 20.5 + -9x + x2 = 0 + 20.5

Combine like terms: -20.5 + 20.5 = 0.0
0.0 + -9x + x2 = 0 + 20.5
-9x + x2 = 0 + 20.5

Combine like terms: 0 + 20.5 = 20.5
-9x + x2 = 20.5

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 20.5 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 20.5 + 20.25

Combine like terms: 20.5 + 20.25 = 40.75
20.25 + -9x + x2 = 40.75

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 40.75

Calculate the square root of the right side: 6.383572667

Break this problem into two subproblems by setting 
(x + -4.5) equal to 6.383572667 and -6.383572667.

Subproblem 1

x + -4.5 = 6.383572667 Simplifying x + -4.5 = 6.383572667 Reorder the terms: -4.5 + x = 6.383572667 Solving -4.5 + x = 6.383572667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 6.383572667 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 6.383572667 + 4.5 x = 6.383572667 + 4.5 Combine like terms: 6.383572667 + 4.5 = 10.883572667 x = 10.883572667 Simplifying x = 10.883572667

Subproblem 2

x + -4.5 = -6.383572667 Simplifying x + -4.5 = -6.383572667 Reorder the terms: -4.5 + x = -6.383572667 Solving -4.5 + x = -6.383572667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -6.383572667 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -6.383572667 + 4.5 x = -6.383572667 + 4.5 Combine like terms: -6.383572667 + 4.5 = -1.883572667 x = -1.883572667 Simplifying x = -1.883572667

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.883572667, -1.883572667}

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