16t^2-120t+100=0

Simple and best practice solution for 16t^2-120t+100=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^2-120t+100=0 equation: 


Simplifying
16t2 + -120t + 100 = 0

Reorder the terms:
100 + -120t + 16t2 = 0

Solving
100 + -120t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(25 + -30t + 4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(25 + -30t + 4t2)' equal to zero and attempt to solve:

Simplifying
25 + -30t + 4t2 = 0

Solving
25 + -30t + 4t2 = 0

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

Divide each side by '4'.
6.25 + -7.5t + t2 = 0

Move the constant term to the right:

Add '-6.25' to each side of the equation.
6.25 + -7.5t + -6.25 + t2 = 0 + -6.25

Reorder the terms:
6.25 + -6.25 + -7.5t + t2 = 0 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + -7.5t + t2 = 0 + -6.25
-7.5t + t2 = 0 + -6.25

Combine like terms: 0 + -6.25 = -6.25
-7.5t + t2 = -6.25

The t term is -7.5t.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5t + 14.0625 + t2 = -6.25 + 14.0625

Reorder the terms:
14.0625 + -7.5t + t2 = -6.25 + 14.0625

Combine like terms: -6.25 + 14.0625 = 7.8125
14.0625 + -7.5t + t2 = 7.8125

Factor a perfect square on the left side:
(t + -3.75)(t + -3.75) = 7.8125

Calculate the square root of the right side: 2.795084972

Break this problem into two subproblems by setting 
(t + -3.75) equal to 2.795084972 and -2.795084972.


Subproblem 1
t + -3.75 = 2.795084972

Simplifying
t + -3.75 = 2.795084972

Reorder the terms:
-3.75 + t = 2.795084972

Solving
-3.75 + t = 2.795084972

Solving for variable 't'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + t = 2.795084972 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + t = 2.795084972 + 3.75
t = 2.795084972 + 3.75

Combine like terms: 2.795084972 + 3.75 = 6.545084972
t = 6.545084972

Simplifying
t = 6.545084972


Subproblem 2
t + -3.75 = -2.795084972

Simplifying
t + -3.75 = -2.795084972

Reorder the terms:
-3.75 + t = -2.795084972

Solving
-3.75 + t = -2.795084972

Solving for variable 't'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + t = -2.795084972 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + t = -2.795084972 + 3.75
t = -2.795084972 + 3.75

Combine like terms: -2.795084972 + 3.75 = 0.954915028
t = 0.954915028

Simplifying
t = 0.954915028


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.545084972, 0.954915028}
Solution
t = {6.545084972, 0.954915028}

See similar equations:

| 24-6x=2x+6(-3x-1) | | 40x=60x+2 | | -6x+3=14-3x(3)-12 | | X=28+-8y | | w^2-2w-8=8 | | -3v+3(v+3)=1-2v | | -6x+3=14-3x(.3)-12 | | -6x+3=14-3x(.3)3-12 | | 9x-16=5x-7 | | 1=5.5x-4.9(x^2) | | 27-2n=2(2n+1)-n | | 2=2(6)+b | | 2n+3=32 | | 135=9(-3+m) | | 2x^4+x^3-28x^2=0 | | e^3x-2=7 | | x(2-x)=35 | | 6(x+2)-(x+3)=5 | | 3(x+1)=5x+1 | | -2x-5y=-30 | | 15+p=3(p+6)+5 | | 2(u-6)+5=9 | | 7k+6k-12k+3=16 | | 2+x=-4(3-2x) | | -3(x+1)=8 | | 1-4u=-15 | | 10-19a+6a= | | 1+2x=10x-3 | | 17x+14y=4 | | 4(x+2)+5x=6 | | 24.2+3.14.10.5.10.5= | | 18-4x=2(2x-3) |

Equations solver categories