-16t^2+84t+112=0

Simple and best practice solution for -16t^2+84t+112=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+84t+112=0 equation: 


Simplifying
-16t2 + 84t + 112 = 0

Reorder the terms:
112 + 84t + -16t2 = 0

Solving
112 + 84t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(28 + 21t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(28 + 21t + -4t2)' equal to zero and attempt to solve:

Simplifying
28 + 21t + -4t2 = 0

Solving
28 + 21t + -4t2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-7 + -5.25t + t2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -5.25t + 7 + t2 = 0 + 7

Reorder the terms:
-7 + 7 + -5.25t + t2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -5.25t + t2 = 0 + 7
-5.25t + t2 = 0 + 7

Combine like terms: 0 + 7 = 7
-5.25t + t2 = 7

The t term is -5.25t.  Take half its coefficient (-2.625).
Square it (6.890625) and add it to both sides.

Add '6.890625' to each side of the equation.
-5.25t + 6.890625 + t2 = 7 + 6.890625

Reorder the terms:
6.890625 + -5.25t + t2 = 7 + 6.890625

Combine like terms: 7 + 6.890625 = 13.890625
6.890625 + -5.25t + t2 = 13.890625

Factor a perfect square on the left side:
(t + -2.625)(t + -2.625) = 13.890625

Calculate the square root of the right side: 3.727012879

Break this problem into two subproblems by setting 
(t + -2.625) equal to 3.727012879 and -3.727012879.


Subproblem 1
t + -2.625 = 3.727012879

Simplifying
t + -2.625 = 3.727012879

Reorder the terms:
-2.625 + t = 3.727012879

Solving
-2.625 + t = 3.727012879

Solving for variable 't'.

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

Add '2.625' to each side of the equation.
-2.625 + 2.625 + t = 3.727012879 + 2.625

Combine like terms: -2.625 + 2.625 = 0.000
0.000 + t = 3.727012879 + 2.625
t = 3.727012879 + 2.625

Combine like terms: 3.727012879 + 2.625 = 6.352012879
t = 6.352012879

Simplifying
t = 6.352012879


Subproblem 2
t + -2.625 = -3.727012879

Simplifying
t + -2.625 = -3.727012879

Reorder the terms:
-2.625 + t = -3.727012879

Solving
-2.625 + t = -3.727012879

Solving for variable 't'.

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

Add '2.625' to each side of the equation.
-2.625 + 2.625 + t = -3.727012879 + 2.625

Combine like terms: -2.625 + 2.625 = 0.000
0.000 + t = -3.727012879 + 2.625
t = -3.727012879 + 2.625

Combine like terms: -3.727012879 + 2.625 = -1.102012879
t = -1.102012879

Simplifying
t = -1.102012879


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.352012879, -1.102012879}
Solution
t = {6.352012879, -1.102012879}

See similar equations:

| 6.3/0.9-(-4.1)x(-0.4) | | 8y-2(5+2y)=7y-16 | | 2 = 12(9x+8) | | -3(3x-3)-9=-2(7x+3)-3 | | 16t^2+84t+112=0 | | 3x+6=27+y | | 7y+-42x+7=0 | | -8-6=7x-2-6x | | 6x-(8X+9)=2x-17 | | 9x+16y=-2 | | Sqrtx^2+7=x+1 | | 5*(x+8)=110 | | 26-u=234 | | 41.73/4.00x | | -4(3y+2x)= | | 70=164-v | | 6.78=2X/0.4-X | | 11x-67=77+2x | | x+x+1+x+2+x+3=-74 | | 3=23-5m | | -3(9+-2y+2.5z)+5y+2z=-27 | | 6(ax+3b)= | | 3+3x-1=9x+4-7x | | 14=4g-2 | | -4+(-24)=12 | | x-(3+x)+6=x-2[x-(3x+4)] | | (x-2)^1/2=(28-2x)^1/4 | | 8(3k-7)=64 | | 15x-6=360 | | x+x-1=2x+3 | | x=2y^2-20y+32 | | 9/2.65 |

Equations solver categories