15t^2+150t+10=250

Simple and best practice solution for 15t^2+150t+10=250 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 15t^2+150t+10=250 equation: 


Simplifying
15t2 + 150t + 10 = 250

Reorder the terms:
10 + 150t + 15t2 = 250

Solving
10 + 150t + 15t2 = 250

Solving for variable 't'.

Reorder the terms:
10 + -250 + 150t + 15t2 = 250 + -250

Combine like terms: 10 + -250 = -240
-240 + 150t + 15t2 = 250 + -250

Combine like terms: 250 + -250 = 0
-240 + 150t + 15t2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(-16 + 10t + t2) = 0

Ignore the factor 15.

Subproblem 1
Set the factor '(-16 + 10t + t2)' equal to zero and attempt to solve:

Simplifying
-16 + 10t + t2 = 0

Solving
-16 + 10t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 10t + 16 + t2 = 0 + 16

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

Combine like terms: -16 + 16 = 0
0 + 10t + t2 = 0 + 16
10t + t2 = 0 + 16

Combine like terms: 0 + 16 = 16
10t + t2 = 16

The t term is 10t.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10t + 25 + t2 = 16 + 25

Reorder the terms:
25 + 10t + t2 = 16 + 25

Combine like terms: 16 + 25 = 41
25 + 10t + t2 = 41

Factor a perfect square on the left side:
(t + 5)(t + 5) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(t + 5) equal to 6.403124237 and -6.403124237.


Subproblem 1
t + 5 = 6.403124237

Simplifying
t + 5 = 6.403124237

Reorder the terms:
5 + t = 6.403124237

Solving
5 + t = 6.403124237

Solving for variable 't'.

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

Add '-5' to each side of the equation.
5 + -5 + t = 6.403124237 + -5

Combine like terms: 5 + -5 = 0
0 + t = 6.403124237 + -5
t = 6.403124237 + -5

Combine like terms: 6.403124237 + -5 = 1.403124237
t = 1.403124237

Simplifying
t = 1.403124237


Subproblem 2
t + 5 = -6.403124237

Simplifying
t + 5 = -6.403124237

Reorder the terms:
5 + t = -6.403124237

Solving
5 + t = -6.403124237

Solving for variable 't'.

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

Add '-5' to each side of the equation.
5 + -5 + t = -6.403124237 + -5

Combine like terms: 5 + -5 = 0
0 + t = -6.403124237 + -5
t = -6.403124237 + -5

Combine like terms: -6.403124237 + -5 = -11.403124237
t = -11.403124237

Simplifying
t = -11.403124237


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.403124237, -11.403124237}
Solution
t = {1.403124237, -11.403124237}

See similar equations:

| W+14=38.4 | | -1-3(4a-8)=-3a-2(-2-2a) | | 10y=2 | | 75-9y=5(-4+2y) | | 91=13y | | 3x+2=8x-3 | | 5u-7=-43 | | a-7b+5C= | | T-6.25=9.33 | | y-5=2(3) | | y-5=2(2) | | log(3x)=log(5)+log(x-2) | | 4(3y+2)=44 | | 4b-3+3b=-4+2b | | -7(x+1)= | | 5u-7=-45 | | N+5.8=27.1 | | y-5=2(1) | | 4+3(1-7k)=-6k+22 | | 4p-5+p=7+5p+2 | | 6-3d=5(2y+3) | | y-5=2x | | x+8+6x=78 | | 7.5x=1500 | | 9-3n-15=30 | | 16-3(-6)= | | 6r=198 | | 3(a+5)=21 | | 3(4x+8)= | | 27g=81 | | E-11.5=30 | | h-e-l-l-o=b |

Equations solver categories