16t^2-31t-4=0

Simple and best practice solution for 16t^2-31t-4=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 16t^2-31t-4=0 equation:


Simplifying
16t2 + -31t + -4 = 0

Reorder the terms:
-4 + -31t + 16t2 = 0

Solving
-4 + -31t + 16t2 = 0

Solving for variable 't'.

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

Divide each side by '16'.
-0.25 + -1.9375t + t2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -1.9375t + 0.25 + t2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -1.9375t + t2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -1.9375t + t2 = 0 + 0.25
-1.9375t + t2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-1.9375t + t2 = 0.25

The t term is -1.9375t.  Take half its coefficient (-0.96875).
Square it (0.9384765625) and add it to both sides.

Add '0.9384765625' to each side of the equation.
-1.9375t + 0.9384765625 + t2 = 0.25 + 0.9384765625

Reorder the terms:
0.9384765625 + -1.9375t + t2 = 0.25 + 0.9384765625

Combine like terms: 0.25 + 0.9384765625 = 1.1884765625
0.9384765625 + -1.9375t + t2 = 1.1884765625

Factor a perfect square on the left side:
(t + -0.96875)(t + -0.96875) = 1.1884765625

Calculate the square root of the right side: 1.090172721

Break this problem into two subproblems by setting 
(t + -0.96875) equal to 1.090172721 and -1.090172721.

Subproblem 1

t + -0.96875 = 1.090172721 Simplifying t + -0.96875 = 1.090172721 Reorder the terms: -0.96875 + t = 1.090172721 Solving -0.96875 + t = 1.090172721 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.96875' to each side of the equation. -0.96875 + 0.96875 + t = 1.090172721 + 0.96875 Combine like terms: -0.96875 + 0.96875 = 0.00000 0.00000 + t = 1.090172721 + 0.96875 t = 1.090172721 + 0.96875 Combine like terms: 1.090172721 + 0.96875 = 2.058922721 t = 2.058922721 Simplifying t = 2.058922721

Subproblem 2

t + -0.96875 = -1.090172721 Simplifying t + -0.96875 = -1.090172721 Reorder the terms: -0.96875 + t = -1.090172721 Solving -0.96875 + t = -1.090172721 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.96875' to each side of the equation. -0.96875 + 0.96875 + t = -1.090172721 + 0.96875 Combine like terms: -0.96875 + 0.96875 = 0.00000 0.00000 + t = -1.090172721 + 0.96875 t = -1.090172721 + 0.96875 Combine like terms: -1.090172721 + 0.96875 = -0.121422721 t = -0.121422721 Simplifying t = -0.121422721

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.058922721, -0.121422721}

See similar equations:

| 16x^2+24x=40 | | 5w-4=-7(w+4) | | -4c+84=112 | | .0875(x)+x=1500 | | 6x+(6+4x)=26 | | 89+7=n+12 | | -4c+84=113 | | -9(-6x+8)=574 | | 4x-6=2(7x+17) | | (N-10)+(9n-3)= | | 11y-12+115=180 | | 6+(6+4x)=26 | | 4b-13=51 | | 2x^3-6x^2+x-3=0 | | 63-4y=11 | | X^2+8-7x=o | | 7=7+k | | 5(x+2)-3x=2(5+x) | | 6(4x-5)(4x-5)= | | 2x+37=6x+9 | | 4x-3+5-2x+3+1= | | -2(4s-6)-12=-2(7s+9)-3 | | 6(7-2x)=3(5p+1) | | 6(-6x-5)=258 | | 6[n+4]=-18 | | -93=-1-2(5m+6) | | 60x^2=18 | | (2z-9)(3+z)=0 | | x+7x+15x=29x+10 | | 18+2a=6-6a | | 4x^3-51x^2-180x+11= | | -4x-10=22 |

Equations solver categories