16t^2-10t-314=0

Simple and best practice solution for 16t^2-10t-314=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^2-10t-314=0 equation:


Simplifying
16t2 + -10t + -314 = 0

Reorder the terms:
-314 + -10t + 16t2 = 0

Solving
-314 + -10t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-157 + -5t + 8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-157 + -5t + 8t2)' equal to zero and attempt to solve:

Simplifying
-157 + -5t + 8t2 = 0

Solving
-157 + -5t + 8t2 = 0

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

Divide each side by '8'.
-19.625 + -0.625t + t2 = 0

Move the constant term to the right:

Add '19.625' to each side of the equation.
-19.625 + -0.625t + 19.625 + t2 = 0 + 19.625

Reorder the terms:
-19.625 + 19.625 + -0.625t + t2 = 0 + 19.625

Combine like terms: -19.625 + 19.625 = 0.000
0.000 + -0.625t + t2 = 0 + 19.625
-0.625t + t2 = 0 + 19.625

Combine like terms: 0 + 19.625 = 19.625
-0.625t + t2 = 19.625

The t term is -0.625t.  Take half its coefficient (-0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
-0.625t + 0.09765625 + t2 = 19.625 + 0.09765625

Reorder the terms:
0.09765625 + -0.625t + t2 = 19.625 + 0.09765625

Combine like terms: 19.625 + 0.09765625 = 19.72265625
0.09765625 + -0.625t + t2 = 19.72265625

Factor a perfect square on the left side:
(t + -0.3125)(t + -0.3125) = 19.72265625

Calculate the square root of the right side: 4.441019731

Break this problem into two subproblems by setting 
(t + -0.3125) equal to 4.441019731 and -4.441019731.


Subproblem 1
t + -0.3125 = 4.441019731

Simplifying
t + -0.3125 = 4.441019731

Reorder the terms:
-0.3125 + t = 4.441019731

Solving
-0.3125 + t = 4.441019731

Solving for variable 't'.

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

Add '0.3125' to each side of the equation.
-0.3125 + 0.3125 + t = 4.441019731 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + t = 4.441019731 + 0.3125
t = 4.441019731 + 0.3125

Combine like terms: 4.441019731 + 0.3125 = 4.753519731
t = 4.753519731

Simplifying
t = 4.753519731


Subproblem 2
t + -0.3125 = -4.441019731

Simplifying
t + -0.3125 = -4.441019731

Reorder the terms:
-0.3125 + t = -4.441019731

Solving
-0.3125 + t = -4.441019731

Solving for variable 't'.

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

Add '0.3125' to each side of the equation.
-0.3125 + 0.3125 + t = -4.441019731 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + t = -4.441019731 + 0.3125
t = -4.441019731 + 0.3125

Combine like terms: -4.441019731 + 0.3125 = -4.128519731
t = -4.128519731

Simplifying
t = -4.128519731


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.753519731, -4.128519731}
Solution
t = {4.753519731, -4.128519731}

See similar equations:

| 4k^2=380 | | 6t^2+4686t-5000=0 | | 8x-14=10x+10 | | 4-6(2x-3)=3x-8 | | 2[x+3(x)]=18 | | 3(4x+1)=3+12x-5 | | 6m-8=2+9m-6-1 | | x+0.01x=212 | | 25n^2+10n-3= | | 25=8+2n | | 6(n-1)=-2n+26 | | 5X+2x=4x-9 | | 68=3(2x+21) | | 0.1x+0.05(x+12)=2.70 | | -(x+13)=-18 | | -3x+45=75 | | 5(4u+2)-14= | | 5u+8w=2u-3 | | 12(4+x)=28x | | 0=2/3x-2 | | 51=2x-23 | | 105p^2-7p-42= | | 4xy=6xy | | x+8x=4.65 | | -16t^2+1074.667t-5000=0 | | x+x+8=4.65 | | x(x+8)=4.65 | | 8+4(1+3n)=-18+6n | | 2+10=4 | | x+(x+8)=4.65 | | 2n=4-3(n+8) | | 3r^2+13r+4= |

Equations solver categories