2x^2+18x=1

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Solution for 2x^2+18x=1 equation:


Simplifying
2x2 + 18x = 1

Reorder the terms:
18x + 2x2 = 1

Solving
18x + 2x2 = 1

Solving for variable 'x'.

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

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

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

Divide each side by '2'.
-0.5 + 9x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 9x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 9x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 9x + x2 = 0 + 0.5
9x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
9x + x2 = 0.5

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 = 0.5 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 0.5 + 20.25

Combine like terms: 0.5 + 20.25 = 20.75
20.25 + 9x + x2 = 20.75

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 20.75

Calculate the square root of the right side: 4.55521679

Break this problem into two subproblems by setting 
(x + 4.5) equal to 4.55521679 and -4.55521679.

Subproblem 1

x + 4.5 = 4.55521679 Simplifying x + 4.5 = 4.55521679 Reorder the terms: 4.5 + x = 4.55521679 Solving 4.5 + x = 4.55521679 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 = 4.55521679 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.55521679 + -4.5 x = 4.55521679 + -4.5 Combine like terms: 4.55521679 + -4.5 = 0.05521679 x = 0.05521679 Simplifying x = 0.05521679

Subproblem 2

x + 4.5 = -4.55521679 Simplifying x + 4.5 = -4.55521679 Reorder the terms: 4.5 + x = -4.55521679 Solving 4.5 + x = -4.55521679 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 = -4.55521679 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.55521679 + -4.5 x = -4.55521679 + -4.5 Combine like terms: -4.55521679 + -4.5 = -9.05521679 x = -9.05521679 Simplifying x = -9.05521679

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.05521679, -9.05521679}

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