7s^2-2s-6=0

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Solution for 7s^2-2s-6=0 equation:


Simplifying
7s2 + -2s + -6 = 0

Reorder the terms:
-6 + -2s + 7s2 = 0

Solving
-6 + -2s + 7s2 = 0

Solving for variable 's'.

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

Divide each side by '7'.
-0.8571428571 + -0.2857142857s + s2 = 0

Move the constant term to the right:

Add '0.8571428571' to each side of the equation.
-0.8571428571 + -0.2857142857s + 0.8571428571 + s2 = 0 + 0.8571428571

Reorder the terms:
-0.8571428571 + 0.8571428571 + -0.2857142857s + s2 = 0 + 0.8571428571

Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000
0.0000000000 + -0.2857142857s + s2 = 0 + 0.8571428571
-0.2857142857s + s2 = 0 + 0.8571428571

Combine like terms: 0 + 0.8571428571 = 0.8571428571
-0.2857142857s + s2 = 0.8571428571

The s term is -0.2857142857s.  Take half its coefficient (-0.1428571429).
Square it (0.02040816328) and add it to both sides.

Add '0.02040816328' to each side of the equation.
-0.2857142857s + 0.02040816328 + s2 = 0.8571428571 + 0.02040816328

Reorder the terms:
0.02040816328 + -0.2857142857s + s2 = 0.8571428571 + 0.02040816328

Combine like terms: 0.8571428571 + 0.02040816328 = 0.87755102038
0.02040816328 + -0.2857142857s + s2 = 0.87755102038

Factor a perfect square on the left side:
(s + -0.1428571429)(s + -0.1428571429) = 0.87755102038

Calculate the square root of the right side: 0.936776932

Break this problem into two subproblems by setting 
(s + -0.1428571429) equal to 0.936776932 and -0.936776932.

Subproblem 1

s + -0.1428571429 = 0.936776932 Simplifying s + -0.1428571429 = 0.936776932 Reorder the terms: -0.1428571429 + s = 0.936776932 Solving -0.1428571429 + s = 0.936776932 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + s = 0.936776932 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + s = 0.936776932 + 0.1428571429 s = 0.936776932 + 0.1428571429 Combine like terms: 0.936776932 + 0.1428571429 = 1.0796340749 s = 1.0796340749 Simplifying s = 1.0796340749

Subproblem 2

s + -0.1428571429 = -0.936776932 Simplifying s + -0.1428571429 = -0.936776932 Reorder the terms: -0.1428571429 + s = -0.936776932 Solving -0.1428571429 + s = -0.936776932 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + s = -0.936776932 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + s = -0.936776932 + 0.1428571429 s = -0.936776932 + 0.1428571429 Combine like terms: -0.936776932 + 0.1428571429 = -0.7939197891 s = -0.7939197891 Simplifying s = -0.7939197891

Solution

The solution to the problem is based on the solutions from the subproblems. s = {1.0796340749, -0.7939197891}

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