2x^2+17x-4=0

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Solution for 2x^2+17x-4=0 equation:


Simplifying
2x2 + 17x + -4 = 0

Reorder the terms:
-4 + 17x + 2x2 = 0

Solving
-4 + 17x + 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 + 8.5x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 8.5x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 8.5x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 8.5x + x2 = 0 + 2
8.5x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
8.5x + x2 = 2

The x term is 8.5x.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5x + 18.0625 + x2 = 2 + 18.0625

Reorder the terms:
18.0625 + 8.5x + x2 = 2 + 18.0625

Combine like terms: 2 + 18.0625 = 20.0625
18.0625 + 8.5x + x2 = 20.0625

Factor a perfect square on the left side:
(x + 4.25)(x + 4.25) = 20.0625

Calculate the square root of the right side: 4.479118217

Break this problem into two subproblems by setting 
(x + 4.25) equal to 4.479118217 and -4.479118217.

Subproblem 1

x + 4.25 = 4.479118217 Simplifying x + 4.25 = 4.479118217 Reorder the terms: 4.25 + x = 4.479118217 Solving 4.25 + x = 4.479118217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 4.479118217 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 4.479118217 + -4.25 x = 4.479118217 + -4.25 Combine like terms: 4.479118217 + -4.25 = 0.229118217 x = 0.229118217 Simplifying x = 0.229118217

Subproblem 2

x + 4.25 = -4.479118217 Simplifying x + 4.25 = -4.479118217 Reorder the terms: 4.25 + x = -4.479118217 Solving 4.25 + x = -4.479118217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -4.479118217 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -4.479118217 + -4.25 x = -4.479118217 + -4.25 Combine like terms: -4.479118217 + -4.25 = -8.729118217 x = -8.729118217 Simplifying x = -8.729118217

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.229118217, -8.729118217}

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