2x^2+18x-5=0

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Solution for 2x^2+18x-5=0 equation:


Simplifying
2x2 + 18x + -5 = 0

Reorder the terms:
-5 + 18x + 2x2 = 0

Solving
-5 + 18x + 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'.
-2.5 + 9x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 9x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 9x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 9x + x2 = 0 + 2.5
9x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
9x + x2 = 2.5

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 = 2.5 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 2.5 + 20.25

Combine like terms: 2.5 + 20.25 = 22.75
20.25 + 9x + x2 = 22.75

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 22.75

Calculate the square root of the right side: 4.769696007

Break this problem into two subproblems by setting 
(x + 4.5) equal to 4.769696007 and -4.769696007.

Subproblem 1

x + 4.5 = 4.769696007 Simplifying x + 4.5 = 4.769696007 Reorder the terms: 4.5 + x = 4.769696007 Solving 4.5 + x = 4.769696007 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 = 4.769696007 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 4.769696007 + -4.5 x = 4.769696007 + -4.5 Combine like terms: 4.769696007 + -4.5 = 0.269696007 x = 0.269696007 Simplifying x = 0.269696007

Subproblem 2

x + 4.5 = -4.769696007 Simplifying x + 4.5 = -4.769696007 Reorder the terms: 4.5 + x = -4.769696007 Solving 4.5 + x = -4.769696007 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 = -4.769696007 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -4.769696007 + -4.5 x = -4.769696007 + -4.5 Combine like terms: -4.769696007 + -4.5 = -9.269696007 x = -9.269696007 Simplifying x = -9.269696007

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.269696007, -9.269696007}

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