7x^2+17x-6=0

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Solution for 7x^2+17x-6=0 equation:


Simplifying
7x2 + 17x + -6 = 0

Reorder the terms:
-6 + 17x + 7x2 = 0

Solving
-6 + 17x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-0.8571428571 + 2.428571429x + x2 = 0

Move the constant term to the right:

Add '0.8571428571' to each side of the equation.
-0.8571428571 + 2.428571429x + 0.8571428571 + x2 = 0 + 0.8571428571

Reorder the terms:
-0.8571428571 + 0.8571428571 + 2.428571429x + x2 = 0 + 0.8571428571

Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000
0.0000000000 + 2.428571429x + x2 = 0 + 0.8571428571
2.428571429x + x2 = 0 + 0.8571428571

Combine like terms: 0 + 0.8571428571 = 0.8571428571
2.428571429x + x2 = 0.8571428571

The x term is 2.428571429x.  Take half its coefficient (1.214285715).
Square it (1.474489798) and add it to both sides.

Add '1.474489798' to each side of the equation.
2.428571429x + 1.474489798 + x2 = 0.8571428571 + 1.474489798

Reorder the terms:
1.474489798 + 2.428571429x + x2 = 0.8571428571 + 1.474489798

Combine like terms: 0.8571428571 + 1.474489798 = 2.3316326551
1.474489798 + 2.428571429x + x2 = 2.3316326551

Factor a perfect square on the left side:
(x + 1.214285715)(x + 1.214285715) = 2.3316326551

Calculate the square root of the right side: 1.526968453

Break this problem into two subproblems by setting 
(x + 1.214285715) equal to 1.526968453 and -1.526968453.

Subproblem 1

x + 1.214285715 = 1.526968453 Simplifying x + 1.214285715 = 1.526968453 Reorder the terms: 1.214285715 + x = 1.526968453 Solving 1.214285715 + x = 1.526968453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.214285715' to each side of the equation. 1.214285715 + -1.214285715 + x = 1.526968453 + -1.214285715 Combine like terms: 1.214285715 + -1.214285715 = 0.000000000 0.000000000 + x = 1.526968453 + -1.214285715 x = 1.526968453 + -1.214285715 Combine like terms: 1.526968453 + -1.214285715 = 0.312682738 x = 0.312682738 Simplifying x = 0.312682738

Subproblem 2

x + 1.214285715 = -1.526968453 Simplifying x + 1.214285715 = -1.526968453 Reorder the terms: 1.214285715 + x = -1.526968453 Solving 1.214285715 + x = -1.526968453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.214285715' to each side of the equation. 1.214285715 + -1.214285715 + x = -1.526968453 + -1.214285715 Combine like terms: 1.214285715 + -1.214285715 = 0.000000000 0.000000000 + x = -1.526968453 + -1.214285715 x = -1.526968453 + -1.214285715 Combine like terms: -1.526968453 + -1.214285715 = -2.741254168 x = -2.741254168 Simplifying x = -2.741254168

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.312682738, -2.741254168}

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