6s^2-13s-6=0

Simple and best practice solution for 6s^2-13s-6=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 6s^2-13s-6=0 equation:


Simplifying
6s2 + -13s + -6 = 0

Reorder the terms:
-6 + -13s + 6s2 = 0

Solving
-6 + -13s + 6s2 = 0

Solving for variable 's'.

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

Divide each side by '6'.
-1 + -2.166666667s + s2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2.166666667s + 1 + s2 = 0 + 1

Reorder the terms:
-1 + 1 + -2.166666667s + s2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2.166666667s + s2 = 0 + 1
-2.166666667s + s2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2.166666667s + s2 = 1

The s term is -2.166666667s.  Take half its coefficient (-1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
-2.166666667s + 1.173611113 + s2 = 1 + 1.173611113

Reorder the terms:
1.173611113 + -2.166666667s + s2 = 1 + 1.173611113

Combine like terms: 1 + 1.173611113 = 2.173611113
1.173611113 + -2.166666667s + s2 = 2.173611113

Factor a perfect square on the left side:
(s + -1.083333334)(s + -1.083333334) = 2.173611113

Calculate the square root of the right side: 1.474317168

Break this problem into two subproblems by setting 
(s + -1.083333334) equal to 1.474317168 and -1.474317168.

Subproblem 1

s + -1.083333334 = 1.474317168 Simplifying s + -1.083333334 = 1.474317168 Reorder the terms: -1.083333334 + s = 1.474317168 Solving -1.083333334 + s = 1.474317168 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + s = 1.474317168 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + s = 1.474317168 + 1.083333334 s = 1.474317168 + 1.083333334 Combine like terms: 1.474317168 + 1.083333334 = 2.557650502 s = 2.557650502 Simplifying s = 2.557650502

Subproblem 2

s + -1.083333334 = -1.474317168 Simplifying s + -1.083333334 = -1.474317168 Reorder the terms: -1.083333334 + s = -1.474317168 Solving -1.083333334 + s = -1.474317168 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + s = -1.474317168 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + s = -1.474317168 + 1.083333334 s = -1.474317168 + 1.083333334 Combine like terms: -1.474317168 + 1.083333334 = -0.390983834 s = -0.390983834 Simplifying s = -0.390983834

Solution

The solution to the problem is based on the solutions from the subproblems. s = {2.557650502, -0.390983834}

See similar equations:

| 11.4p=91.3 | | b+6=-6 | | 2(5x+4)=4x+3 | | 41=3-5x | | 36=-4k | | 51-(-7)= | | -1.9p=17.1 | | -7h=-70 | | 12-2x=-4(x-3) | | 3(x+5)=2(3x-15) | | 9y=3x+1 | | 16t^2+64=h | | 84=7v | | -13+3+30=12r-4r+2-9-5r | | 1*-2= | | -8.1p=-32.4 | | 120000x-3000x^2=0 | | 5.7p=51.3 | | 10-2x-5=5x+10-5x+11 | | 5(-2x-2)+4x=-2x | | 1.2x+2.7=63 | | 4.9p=34.3 | | (18x^2)-(1.2x^2)=0 | | -17+(-5)*6= | | 18x^2-1.2x^2=0 | | 26-7=16 | | 12x^3+39x^2-36x= | | 106y-300=71 | | 8.7p=104.4 | | 6(x-2)=3(1+2x) | | 2b^3-5b^2-18b+45=0 | | 2b^3-5b^2-18b+45= |

Equations solver categories