187=16t^2+32t

Simple and best practice solution for 187=16t^2+32t 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 187=16t^2+32t equation:


Simplifying
187 = 16t2 + 32t

Reorder the terms:
187 = 32t + 16t2

Solving
187 = 32t + 16t2

Solving for variable 't'.

Reorder the terms:
187 + -32t + -16t2 = 32t + -32t + 16t2 + -16t2

Combine like terms: 32t + -32t = 0
187 + -32t + -16t2 = 0 + 16t2 + -16t2
187 + -32t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
187 + -32t + -16t2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-11.6875 + 2t + t2 = 0

Move the constant term to the right:

Add '11.6875' to each side of the equation.
-11.6875 + 2t + 11.6875 + t2 = 0 + 11.6875

Reorder the terms:
-11.6875 + 11.6875 + 2t + t2 = 0 + 11.6875

Combine like terms: -11.6875 + 11.6875 = 0.0000
0.0000 + 2t + t2 = 0 + 11.6875
2t + t2 = 0 + 11.6875

Combine like terms: 0 + 11.6875 = 11.6875
2t + t2 = 11.6875

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = 11.6875 + 1

Reorder the terms:
1 + 2t + t2 = 11.6875 + 1

Combine like terms: 11.6875 + 1 = 12.6875
1 + 2t + t2 = 12.6875

Factor a perfect square on the left side:
(t + 1)(t + 1) = 12.6875

Calculate the square root of the right side: 3.561951712

Break this problem into two subproblems by setting 
(t + 1) equal to 3.561951712 and -3.561951712.

Subproblem 1

t + 1 = 3.561951712 Simplifying t + 1 = 3.561951712 Reorder the terms: 1 + t = 3.561951712 Solving 1 + t = 3.561951712 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 3.561951712 + -1 Combine like terms: 1 + -1 = 0 0 + t = 3.561951712 + -1 t = 3.561951712 + -1 Combine like terms: 3.561951712 + -1 = 2.561951712 t = 2.561951712 Simplifying t = 2.561951712

Subproblem 2

t + 1 = -3.561951712 Simplifying t + 1 = -3.561951712 Reorder the terms: 1 + t = -3.561951712 Solving 1 + t = -3.561951712 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = -3.561951712 + -1 Combine like terms: 1 + -1 = 0 0 + t = -3.561951712 + -1 t = -3.561951712 + -1 Combine like terms: -3.561951712 + -1 = -4.561951712 t = -4.561951712 Simplifying t = -4.561951712

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.561951712, -4.561951712}

See similar equations:

| 3(8+4x)=36 | | (-5x^3y^3)(2xy^4)=equation | | x/4=-41 | | -41=x/4 | | (-75)/25= | | 4y-8=3-(y+1) | | 5(3+x)=15 | | 2x^2-20x=-49 | | 12x+5y=827 | | -4(2-7x)=244 | | 3x+14=x-12 | | 37=-v/6 | | -5-(+6)= | | 1/4(t+4)=48 | | 1/20(x+53)=20 | | 25x+10Y=56 | | 1/20(x+53)=27 | | 9+2x=-4x+3 | | -2/3x+12=-44 | | 4x-1=107-3x | | -4x-2-2x=64 | | -4-x/-3=7 | | 9y=-17 | | 2(t-1)-3(2t-5)=3-5(4t+1) | | -17=9y | | 2X+10+3x-50=180 | | 3=z+17 | | 2(x-4)=7x-7-5x | | -v/2=43 | | 0.3x= | | -43=-v/5 | | 9.3*10*10*10*10*10*10*10= |

Equations solver categories