5t^2+15t+1=11

Simple and best practice solution for 5t^2+15t+1=11 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 5t^2+15t+1=11 equation: 


Simplifying
5t2 + 15t + 1 = 11

Reorder the terms:
1 + 15t + 5t2 = 11

Solving
1 + 15t + 5t2 = 11

Solving for variable 't'.

Reorder the terms:
1 + -11 + 15t + 5t2 = 11 + -11

Combine like terms: 1 + -11 = -10
-10 + 15t + 5t2 = 11 + -11

Combine like terms: 11 + -11 = 0
-10 + 15t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-2 + 3t + t2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-2 + 3t + t2)' equal to zero and attempt to solve:

Simplifying
-2 + 3t + t2 = 0

Solving
-2 + 3t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 3t + 2 + t2 = 0 + 2

Reorder the terms:
-2 + 2 + 3t + t2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3t + t2 = 0 + 2
3t + t2 = 0 + 2

Combine like terms: 0 + 2 = 2
3t + t2 = 2

The t term is 3t.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3t + 2.25 + t2 = 2 + 2.25

Reorder the terms:
2.25 + 3t + t2 = 2 + 2.25

Combine like terms: 2 + 2.25 = 4.25
2.25 + 3t + t2 = 4.25

Factor a perfect square on the left side:
(t + 1.5)(t + 1.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(t + 1.5) equal to 2.061552813 and -2.061552813.


Subproblem 1
t + 1.5 = 2.061552813

Simplifying
t + 1.5 = 2.061552813

Reorder the terms:
1.5 + t = 2.061552813

Solving
1.5 + t = 2.061552813

Solving for variable 't'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + t = 2.061552813 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + t = 2.061552813 + -1.5
t = 2.061552813 + -1.5

Combine like terms: 2.061552813 + -1.5 = 0.561552813
t = 0.561552813

Simplifying
t = 0.561552813


Subproblem 2
t + 1.5 = -2.061552813

Simplifying
t + 1.5 = -2.061552813

Reorder the terms:
1.5 + t = -2.061552813

Solving
1.5 + t = -2.061552813

Solving for variable 't'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + t = -2.061552813 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + t = -2.061552813 + -1.5
t = -2.061552813 + -1.5

Combine like terms: -2.061552813 + -1.5 = -3.561552813
t = -3.561552813

Simplifying
t = -3.561552813


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.561552813, -3.561552813}
Solution
t = {0.561552813, -3.561552813}

See similar equations:

| 7.08x+42.48=84.96 | | 100x-5000=75x-10000 | | -2x^2=2x-40 | | 30x+(31-x)*20=810 | | Log(3x+10)=2 | | 20.62=0.75x+4.12 | | log(3x+4)=3 | | F(-2)=4x+1 | | 352=6x+280 | | .50=-2x+6 | | 2(x-11)=15-4x | | 5x-11y=14.25 | | 3*x-2*(.6666666666*x-7)=19 | | 4.92x+100=24.2064+10x | | N+3+3=11+2n-6+8 | | 12j-12j+2j+j=12 | | (k+3)(k-3)=20 | | 2a-a=13 | | 2p+4=28 | | ln(8x-1)=ln(x)+ln(6) | | 18q-17q=5 | | 5x+41=66 | | -3+24= | | -3[2-3(x+2)+5x]=4x-3+2x+3 | | 11a+14a=3(a+11) | | ln(8x)-ln(1)=ln(x)+ln(6) | | 6x^2+8x=18 | | 3x-2(x+1)-1=5(x-1)+2 | | 30x-(31-x)=810 | | (-7x)=49 | | 3h-5=5h+17 | | 15-5d-7(d-2)=5d-22 |

Equations solver categories