16t^2+108t+160=0

Simple and best practice solution for 16t^2+108t+160=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+108t+160=0 equation: 


Simplifying
16t2 + 108t + 160 = 0

Reorder the terms:
160 + 108t + 16t2 = 0

Solving
160 + 108t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(40 + 27t + 4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(40 + 27t + 4t2)' equal to zero and attempt to solve:

Simplifying
40 + 27t + 4t2 = 0

Solving
40 + 27t + 4t2 = 0

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

Divide each side by '4'.
10 + 6.75t + t2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 6.75t + -10 + t2 = 0 + -10

Reorder the terms:
10 + -10 + 6.75t + t2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 6.75t + t2 = 0 + -10
6.75t + t2 = 0 + -10

Combine like terms: 0 + -10 = -10
6.75t + t2 = -10

The t term is 6.75t.  Take half its coefficient (3.375).
Square it (11.390625) and add it to both sides.

Add '11.390625' to each side of the equation.
6.75t + 11.390625 + t2 = -10 + 11.390625

Reorder the terms:
11.390625 + 6.75t + t2 = -10 + 11.390625

Combine like terms: -10 + 11.390625 = 1.390625
11.390625 + 6.75t + t2 = 1.390625

Factor a perfect square on the left side:
(t + 3.375)(t + 3.375) = 1.390625

Calculate the square root of the right side: 1.179247642

Break this problem into two subproblems by setting 
(t + 3.375) equal to 1.179247642 and -1.179247642.


Subproblem 1
t + 3.375 = 1.179247642

Simplifying
t + 3.375 = 1.179247642

Reorder the terms:
3.375 + t = 1.179247642

Solving
3.375 + t = 1.179247642

Solving for variable 't'.

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

Add '-3.375' to each side of the equation.
3.375 + -3.375 + t = 1.179247642 + -3.375

Combine like terms: 3.375 + -3.375 = 0.000
0.000 + t = 1.179247642 + -3.375
t = 1.179247642 + -3.375

Combine like terms: 1.179247642 + -3.375 = -2.195752358
t = -2.195752358

Simplifying
t = -2.195752358


Subproblem 2
t + 3.375 = -1.179247642

Simplifying
t + 3.375 = -1.179247642

Reorder the terms:
3.375 + t = -1.179247642

Solving
3.375 + t = -1.179247642

Solving for variable 't'.

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

Add '-3.375' to each side of the equation.
3.375 + -3.375 + t = -1.179247642 + -3.375

Combine like terms: 3.375 + -3.375 = 0.000
0.000 + t = -1.179247642 + -3.375
t = -1.179247642 + -3.375

Combine like terms: -1.179247642 + -3.375 = -4.554247642
t = -4.554247642

Simplifying
t = -4.554247642


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-2.195752358, -4.554247642}
Solution
t = {-2.195752358, -4.554247642}

See similar equations:

| 5v^4-20v^3+25v^2=0 | | x(x-1)(1-x)= | | 5x+4x-3x=17+7 | | 9w^3+12w^2-21w=0 | | 9(3x-1)=4x-5x | | 4y^4-32y^3+64y^2=0 | | 9y^5-42y^4+24y^3=0 | | 7y^7-42y^6+63y^5=0 | | Sin(cosx)=cos(sinx) | | 3(n+1)-8(2-n)=20 | | 2+3x-1=6 | | X+.25=40 | | 5x+x=6x | | x^2-23x+30=0 | | 10=4(z-8)-6 | | P=50-0.2Q | | 12y-28=64 | | -2y-3(3z-6y)-4z= | | 5+2(4-7)= | | 6ab-2a+3ab+7b= | | 45-6y=63 | | x^3-4x^2-8x+24=0 | | x+10+141+115+x+20=360 | | 4y-x=17 | | x^3-4x^2-8x+8=0 | | 5y-4y+1=-7 | | 4x-3=4x+8 | | 2x+7y-11z=42 | | 5x+4-8x=12-19x+16x-8 | | 108+2x+x+5+124=360 | | 73+120+2x+x+5=360 | | x+10+145+x+15+116=360 |

Equations solver categories