2x^2+6x-17=0

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Solution for 2x^2+6x-17=0 equation:


Simplifying
2x2 + 6x + -17 = 0

Reorder the terms:
-17 + 6x + 2x2 = 0

Solving
-17 + 6x + 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'.
-8.5 + 3x + x2 = 0

Move the constant term to the right:

Add '8.5' to each side of the equation.
-8.5 + 3x + 8.5 + x2 = 0 + 8.5

Reorder the terms:
-8.5 + 8.5 + 3x + x2 = 0 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + 3x + x2 = 0 + 8.5
3x + x2 = 0 + 8.5

Combine like terms: 0 + 8.5 = 8.5
3x + x2 = 8.5

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 8.5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 8.5 + 2.25

Combine like terms: 8.5 + 2.25 = 10.75
2.25 + 3x + x2 = 10.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 10.75

Calculate the square root of the right side: 3.278719262

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.278719262 and -3.278719262.

Subproblem 1

x + 1.5 = 3.278719262 Simplifying x + 1.5 = 3.278719262 Reorder the terms: 1.5 + x = 3.278719262 Solving 1.5 + x = 3.278719262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 3.278719262 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.278719262 + -1.5 x = 3.278719262 + -1.5 Combine like terms: 3.278719262 + -1.5 = 1.778719262 x = 1.778719262 Simplifying x = 1.778719262

Subproblem 2

x + 1.5 = -3.278719262 Simplifying x + 1.5 = -3.278719262 Reorder the terms: 1.5 + x = -3.278719262 Solving 1.5 + x = -3.278719262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -3.278719262 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.278719262 + -1.5 x = -3.278719262 + -1.5 Combine like terms: -3.278719262 + -1.5 = -4.778719262 x = -4.778719262 Simplifying x = -4.778719262

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.778719262, -4.778719262}

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