16t^2-72t=81

Simple and best practice solution for 16t^2-72t=81 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^2-72t=81 equation:


Simplifying
16t2 + -72t = 81

Reorder the terms:
-72t + 16t2 = 81

Solving
-72t + 16t2 = 81

Solving for variable 't'.

Reorder the terms:
-81 + -72t + 16t2 = 81 + -81

Combine like terms: 81 + -81 = 0
-81 + -72t + 16t2 = 0

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

Divide each side by '16'.
-5.0625 + -4.5t + t2 = 0

Move the constant term to the right:

Add '5.0625' to each side of the equation.
-5.0625 + -4.5t + 5.0625 + t2 = 0 + 5.0625

Reorder the terms:
-5.0625 + 5.0625 + -4.5t + t2 = 0 + 5.0625

Combine like terms: -5.0625 + 5.0625 = 0.0000
0.0000 + -4.5t + t2 = 0 + 5.0625
-4.5t + t2 = 0 + 5.0625

Combine like terms: 0 + 5.0625 = 5.0625
-4.5t + t2 = 5.0625

The t term is -4.5t.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5t + 5.0625 + t2 = 5.0625 + 5.0625

Reorder the terms:
5.0625 + -4.5t + t2 = 5.0625 + 5.0625

Combine like terms: 5.0625 + 5.0625 = 10.125
5.0625 + -4.5t + t2 = 10.125

Factor a perfect square on the left side:
(t + -2.25)(t + -2.25) = 10.125

Calculate the square root of the right side: 3.181980515

Break this problem into two subproblems by setting 
(t + -2.25) equal to 3.181980515 and -3.181980515.

Subproblem 1

t + -2.25 = 3.181980515 Simplifying t + -2.25 = 3.181980515 Reorder the terms: -2.25 + t = 3.181980515 Solving -2.25 + t = 3.181980515 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + t = 3.181980515 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = 3.181980515 + 2.25 t = 3.181980515 + 2.25 Combine like terms: 3.181980515 + 2.25 = 5.431980515 t = 5.431980515 Simplifying t = 5.431980515

Subproblem 2

t + -2.25 = -3.181980515 Simplifying t + -2.25 = -3.181980515 Reorder the terms: -2.25 + t = -3.181980515 Solving -2.25 + t = -3.181980515 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + t = -3.181980515 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = -3.181980515 + 2.25 t = -3.181980515 + 2.25 Combine like terms: -3.181980515 + 2.25 = -0.931980515 t = -0.931980515 Simplifying t = -0.931980515

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.431980515, -0.931980515}

See similar equations:

| (7X+1)8= | | 1+3b=5b+11 | | 1+t=6t-29 | | 4t+3=-3t+73 | | 2+5k=7k-10 | | d+6=3d-10 | | 7w-2=46+3w | | 7x-10=5x+4 | | a=x+(x*0.25) | | 7x+1(8)= | | -2+6b=5b+0 | | 2n-6=3n-12 | | -n+5=3n+5 | | -1-6k=-2k+19 | | -3x-5=-45-7x | | -x-7=-19+x | | 5x+6=2x+21 | | 5w-5=-113-4w | | -3b+9=-1+7b | | -2k+1=-8-k | | 7-5w=5w+47 | | -7m+1=2m-98 | | 5n+4=4n+10 | | -8+2k=-3k+27 | | 7w+2=-5w-82 | | -6n+10=-4n+2 | | 7w-1=4w+26 | | 4d-8=-5d+91 | | 5-7a=2a+68 | | 2w+6=-54-3w | | -5t+7=-t-33 | | 6d+4=124-6d |

Equations solver categories