6x^2+17x+2=0

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


Simplifying
6x2 + 17x + 2 = 0

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

Solving
2 + 17x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
0.3333333333 + 2.833333333x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 2.833333333x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 2.833333333x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 2.833333333x + x2 = 0 + -0.3333333333
2.833333333x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
2.833333333x + x2 = -0.3333333333

The x term is 2.833333333x.  Take half its coefficient (1.416666667).
Square it (2.006944445) and add it to both sides.

Add '2.006944445' to each side of the equation.
2.833333333x + 2.006944445 + x2 = -0.3333333333 + 2.006944445

Reorder the terms:
2.006944445 + 2.833333333x + x2 = -0.3333333333 + 2.006944445

Combine like terms: -0.3333333333 + 2.006944445 = 1.6736111117
2.006944445 + 2.833333333x + x2 = 1.6736111117

Factor a perfect square on the left side:
(x + 1.416666667)(x + 1.416666667) = 1.6736111117

Calculate the square root of the right side: 1.293681225

Break this problem into two subproblems by setting 
(x + 1.416666667) equal to 1.293681225 and -1.293681225.

Subproblem 1

x + 1.416666667 = 1.293681225 Simplifying x + 1.416666667 = 1.293681225 Reorder the terms: 1.416666667 + x = 1.293681225 Solving 1.416666667 + x = 1.293681225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.416666667' to each side of the equation. 1.416666667 + -1.416666667 + x = 1.293681225 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + x = 1.293681225 + -1.416666667 x = 1.293681225 + -1.416666667 Combine like terms: 1.293681225 + -1.416666667 = -0.122985442 x = -0.122985442 Simplifying x = -0.122985442

Subproblem 2

x + 1.416666667 = -1.293681225 Simplifying x + 1.416666667 = -1.293681225 Reorder the terms: 1.416666667 + x = -1.293681225 Solving 1.416666667 + x = -1.293681225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.416666667' to each side of the equation. 1.416666667 + -1.416666667 + x = -1.293681225 + -1.416666667 Combine like terms: 1.416666667 + -1.416666667 = 0.000000000 0.000000000 + x = -1.293681225 + -1.416666667 x = -1.293681225 + -1.416666667 Combine like terms: -1.293681225 + -1.416666667 = -2.710347892 x = -2.710347892 Simplifying x = -2.710347892

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.122985442, -2.710347892}

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