16t^2+4t+3=21

Simple and best practice solution for 16t^2+4t+3=21 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+4t+3=21 equation: 


Simplifying
16t2 + 4t + 3 = 21

Reorder the terms:
3 + 4t + 16t2 = 21

Solving
3 + 4t + 16t2 = 21

Solving for variable 't'.

Reorder the terms:
3 + -21 + 4t + 16t2 = 21 + -21

Combine like terms: 3 + -21 = -18
-18 + 4t + 16t2 = 21 + -21

Combine like terms: 21 + -21 = 0
-18 + 4t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 2t + 8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + 2t + 8t2)' equal to zero and attempt to solve:

Simplifying
-9 + 2t + 8t2 = 0

Solving
-9 + 2t + 8t2 = 0

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

Divide each side by '8'.
-1.125 + 0.25t + t2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + 0.25t + 1.125 + t2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + 0.25t + t2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + 0.25t + t2 = 0 + 1.125
0.25t + t2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
0.25t + t2 = 1.125

The t term is 0.25t.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25t + 0.015625 + t2 = 1.125 + 0.015625

Reorder the terms:
0.015625 + 0.25t + t2 = 1.125 + 0.015625

Combine like terms: 1.125 + 0.015625 = 1.140625
0.015625 + 0.25t + t2 = 1.140625

Factor a perfect square on the left side:
(t + 0.125)(t + 0.125) = 1.140625

Calculate the square root of the right side: 1.068000468

Break this problem into two subproblems by setting 
(t + 0.125) equal to 1.068000468 and -1.068000468.


Subproblem 1
t + 0.125 = 1.068000468

Simplifying
t + 0.125 = 1.068000468

Reorder the terms:
0.125 + t = 1.068000468

Solving
0.125 + t = 1.068000468

Solving for variable 't'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + t = 1.068000468 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + t = 1.068000468 + -0.125
t = 1.068000468 + -0.125

Combine like terms: 1.068000468 + -0.125 = 0.943000468
t = 0.943000468

Simplifying
t = 0.943000468


Subproblem 2
t + 0.125 = -1.068000468

Simplifying
t + 0.125 = -1.068000468

Reorder the terms:
0.125 + t = -1.068000468

Solving
0.125 + t = -1.068000468

Solving for variable 't'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + t = -1.068000468 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + t = -1.068000468 + -0.125
t = -1.068000468 + -0.125

Combine like terms: -1.068000468 + -0.125 = -1.193000468
t = -1.193000468

Simplifying
t = -1.193000468


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.943000468, -1.193000468}
Solution
t = {0.943000468, -1.193000468}

See similar equations:

| z^2-xy-19= | | 2x^2-13x+8=0byfactoring | | 4(-2k)= | | R-3.7=4.6 | | 9(-2x+9)=3(6x-9) | | 7x^2-11x=84 | | 16t^2+4t+3=0 | | 2x^2-13x+8=0 | | (8+5)*2= | | -5x+10=3(x+4) | | 5(4-3+2)= | | 7-2*(-5)= | | 5x+4=-2x+10 | | M^2+23m-24= | | lx-3l+9=30 | | 16t^2+-40t+3=0 | | 36-x=-x+2 | | 8-7x-6-14x=5 | | 5x-7(x+3)=9 | | 30x-y-5(6x-9y+2z)=30x-y-30x+45y | | 9(x)=5 | | 18x+18y= | | Dz+mt=k | | -40+8x=-8(x+7) | | -2+4(x-1)=3(x+4)-12 | | -7-6=9x+3-8x | | a^15=32 | | 3/4y+2=1/4y+5 | | 27=18-y | | 2(px-1)=99-7(3-4x) | | -6+5(-1-1b)=19 | | (5-2x)(-x)+x*x= |

Equations solver categories