500=4.9t^2+30t

Simple and best practice solution for 500=4.9t^2+30t 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 500=4.9t^2+30t equation:


Simplifying
500 = 4.9t2 + 30t

Reorder the terms:
500 = 30t + 4.9t2

Solving
500 = 30t + 4.9t2

Solving for variable 't'.

Reorder the terms:
500 + -30t + -4.9t2 = 30t + -30t + 4.9t2 + -4.9t2

Combine like terms: 30t + -30t = 0
500 + -30t + -4.9t2 = 0 + 4.9t2 + -4.9t2
500 + -30t + -4.9t2 = 4.9t2 + -4.9t2

Combine like terms: 4.9t2 + -4.9t2 = 0.0
500 + -30t + -4.9t2 = 0.0

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
-102.0408163 + 6.12244898t + t2 = 0

Move the constant term to the right:

Add '102.0408163' to each side of the equation.
-102.0408163 + 6.12244898t + 102.0408163 + t2 = 0 + 102.0408163

Reorder the terms:
-102.0408163 + 102.0408163 + 6.12244898t + t2 = 0 + 102.0408163

Combine like terms: -102.0408163 + 102.0408163 = 0.0000000
0.0000000 + 6.12244898t + t2 = 0 + 102.0408163
6.12244898t + t2 = 0 + 102.0408163

Combine like terms: 0 + 102.0408163 = 102.0408163
6.12244898t + t2 = 102.0408163

The t term is 6.12244898t.  Take half its coefficient (3.06122449).
Square it (9.371095378) and add it to both sides.

Add '9.371095378' to each side of the equation.
6.12244898t + 9.371095378 + t2 = 102.0408163 + 9.371095378

Reorder the terms:
9.371095378 + 6.12244898t + t2 = 102.0408163 + 9.371095378

Combine like terms: 102.0408163 + 9.371095378 = 111.411911678
9.371095378 + 6.12244898t + t2 = 111.411911678

Factor a perfect square on the left side:
(t + 3.06122449)(t + 3.06122449) = 111.411911678

Calculate the square root of the right side: 10.555184114

Break this problem into two subproblems by setting 
(t + 3.06122449) equal to 10.555184114 and -10.555184114.

Subproblem 1

t + 3.06122449 = 10.555184114 Simplifying t + 3.06122449 = 10.555184114 Reorder the terms: 3.06122449 + t = 10.555184114 Solving 3.06122449 + t = 10.555184114 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.06122449' to each side of the equation. 3.06122449 + -3.06122449 + t = 10.555184114 + -3.06122449 Combine like terms: 3.06122449 + -3.06122449 = 0.00000000 0.00000000 + t = 10.555184114 + -3.06122449 t = 10.555184114 + -3.06122449 Combine like terms: 10.555184114 + -3.06122449 = 7.493959624 t = 7.493959624 Simplifying t = 7.493959624

Subproblem 2

t + 3.06122449 = -10.555184114 Simplifying t + 3.06122449 = -10.555184114 Reorder the terms: 3.06122449 + t = -10.555184114 Solving 3.06122449 + t = -10.555184114 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.06122449' to each side of the equation. 3.06122449 + -3.06122449 + t = -10.555184114 + -3.06122449 Combine like terms: 3.06122449 + -3.06122449 = 0.00000000 0.00000000 + t = -10.555184114 + -3.06122449 t = -10.555184114 + -3.06122449 Combine like terms: -10.555184114 + -3.06122449 = -13.616408604 t = -13.616408604 Simplifying t = -13.616408604

Solution

The solution to the problem is based on the solutions from the subproblems. t = {7.493959624, -13.616408604}

See similar equations:

| 5-3x=2x+8 | | 8-3x+3=5-2x+3 | | -8+4v=-15-9 | | 5y-4x+2=0 | | 2.5=-n | | logx=1.86 | | 55x=50(x+3) | | y=6x^2-7x-5 | | 6(2x+3)=72 | | 8h+5-3h=8h-r | | y/4.6=-2.6 | | C(85)=5/9(85−32) | | -2x/5=3/4 | | 48x-2=38 | | 2x/5=1/4 | | (5z^-3/z^-1)5/z^2 | | -9/5x16 | | (5z^-3/z^-1)5÷z^2 | | 7x+0.75=15.75+4x | | x^2+y^2+z^2+2xy+2xz+2yz=0 | | 83x-10/313 | | 0.30x+360=240+0.40x | | x^2+11x+43= | | 0.30x+360=240+0.40 | | x^2+y^2+z^2+2xy+2xz+2yx=0 | | 5x-5=7+3x | | x^2+y^2+z^2=0 | | 49m^2-100n^2=0 | | (2u-15)/-40 | | 6-17x+17x^2-7x^3+x^4=0 | | x-133=394 | | x*20-89+53=240 |

Equations solver categories