3t^2+48t=16

Simple and best practice solution for 3t^2+48t=16 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 3t^2+48t=16 equation: 


Simplifying
3t2 + 48t = 16

Reorder the terms:
48t + 3t2 = 16

Solving
48t + 3t2 = 16

Solving for variable 't'.

Reorder the terms:
-16 + 48t + 3t2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + 48t + 3t2 = 0

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

Divide each side by '3'.
-5.333333333 + 16t + t2 = 0

Move the constant term to the right:

Add '5.333333333' to each side of the equation.
-5.333333333 + 16t + 5.333333333 + t2 = 0 + 5.333333333

Reorder the terms:
-5.333333333 + 5.333333333 + 16t + t2 = 0 + 5.333333333

Combine like terms: -5.333333333 + 5.333333333 = 0.000000000
0.000000000 + 16t + t2 = 0 + 5.333333333
16t + t2 = 0 + 5.333333333

Combine like terms: 0 + 5.333333333 = 5.333333333
16t + t2 = 5.333333333

The t term is 16t.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16t + 64 + t2 = 5.333333333 + 64

Reorder the terms:
64 + 16t + t2 = 5.333333333 + 64

Combine like terms: 5.333333333 + 64 = 69.333333333
64 + 16t + t2 = 69.333333333

Factor a perfect square on the left side:
(t + 8)(t + 8) = 69.333333333

Calculate the square root of the right side: 8.326663998

Break this problem into two subproblems by setting 
(t + 8) equal to 8.326663998 and -8.326663998.


Subproblem 1
t + 8 = 8.326663998

Simplifying
t + 8 = 8.326663998

Reorder the terms:
8 + t = 8.326663998

Solving
8 + t = 8.326663998

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + t = 8.326663998 + -8

Combine like terms: 8 + -8 = 0
0 + t = 8.326663998 + -8
t = 8.326663998 + -8

Combine like terms: 8.326663998 + -8 = 0.326663998
t = 0.326663998

Simplifying
t = 0.326663998


Subproblem 2
t + 8 = -8.326663998

Simplifying
t + 8 = -8.326663998

Reorder the terms:
8 + t = -8.326663998

Solving
8 + t = -8.326663998

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + t = -8.326663998 + -8

Combine like terms: 8 + -8 = 0
0 + t = -8.326663998 + -8
t = -8.326663998 + -8

Combine like terms: -8.326663998 + -8 = -16.326663998
t = -16.326663998

Simplifying
t = -16.326663998


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.326663998, -16.326663998}

See similar equations:

| 5y-21=6x+32 | | 4v-9=47 | | -2(q-5)=-3(q+1) | | 6x+32=180 | | 3t^2+48=16 | | 95k=5 | | 5y-21=180 | | a+b+c+d+e+f+g+h+i+j+k+l+m+n+o+p+q+r+s+t-u-v-w-x-y-z=115513153513+12365x-2x^5 | | 61=3y+16 | | n/25=-8 | | 6t-48=18 | | 2x(x)+24=0 | | 3t^2-48t=0 | | 14y+31=101 | | 6x-8=-132-8x | | 4x+0.5=28.5 | | x/0=2 | | 2x+6=-13 | | 72-n/-2=-88 | | -2*-1/2= | | r=2s+10 | | 11-19=-16-16 | | 2x+6y+7x+2y= | | 10/3=5v | | 3t^2-48t=16 | | 12x-1x+2=3x+3+3 | | 1:2/12= | | x-x-2/12 | | 11-19m=-16m-6 | | 51=-4d+7 | | pi*2x=1 | | 48n+26=-502 |

Equations solver categories