t=-9t^2+27t+2

Simple and best practice solution for t=-9t^2+27t+2 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 t=-9t^2+27t+2 equation:


Simplifying
t = -9t2 + 27t + 2

Reorder the terms:
t = 2 + 27t + -9t2

Solving
t = 2 + 27t + -9t2

Solving for variable 't'.

Reorder the terms:
-2 + t + -27t + 9t2 = 2 + 27t + -9t2 + -2 + -27t + 9t2

Combine like terms: t + -27t = -26t
-2 + -26t + 9t2 = 2 + 27t + -9t2 + -2 + -27t + 9t2

Reorder the terms:
-2 + -26t + 9t2 = 2 + -2 + 27t + -27t + -9t2 + 9t2

Combine like terms: 2 + -2 = 0
-2 + -26t + 9t2 = 0 + 27t + -27t + -9t2 + 9t2
-2 + -26t + 9t2 = 27t + -27t + -9t2 + 9t2

Combine like terms: 27t + -27t = 0
-2 + -26t + 9t2 = 0 + -9t2 + 9t2
-2 + -26t + 9t2 = -9t2 + 9t2

Combine like terms: -9t2 + 9t2 = 0
-2 + -26t + 9t2 = 0

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

Divide each side by '9'.
-0.2222222222 + -2.888888889t + t2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + -2.888888889t + 0.2222222222 + t2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + -2.888888889t + t2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + -2.888888889t + t2 = 0 + 0.2222222222
-2.888888889t + t2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
-2.888888889t + t2 = 0.2222222222

The t term is -2.888888889t.  Take half its coefficient (-1.444444445).
Square it (2.086419755) and add it to both sides.

Add '2.086419755' to each side of the equation.
-2.888888889t + 2.086419755 + t2 = 0.2222222222 + 2.086419755

Reorder the terms:
2.086419755 + -2.888888889t + t2 = 0.2222222222 + 2.086419755

Combine like terms: 0.2222222222 + 2.086419755 = 2.3086419772
2.086419755 + -2.888888889t + t2 = 2.3086419772

Factor a perfect square on the left side:
(t + -1.444444445)(t + -1.444444445) = 2.3086419772

Calculate the square root of the right side: 1.519421593

Break this problem into two subproblems by setting 
(t + -1.444444445) equal to 1.519421593 and -1.519421593.

Subproblem 1

t + -1.444444445 = 1.519421593 Simplifying t + -1.444444445 = 1.519421593 Reorder the terms: -1.444444445 + t = 1.519421593 Solving -1.444444445 + t = 1.519421593 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.444444445' to each side of the equation. -1.444444445 + 1.444444445 + t = 1.519421593 + 1.444444445 Combine like terms: -1.444444445 + 1.444444445 = 0.000000000 0.000000000 + t = 1.519421593 + 1.444444445 t = 1.519421593 + 1.444444445 Combine like terms: 1.519421593 + 1.444444445 = 2.963866038 t = 2.963866038 Simplifying t = 2.963866038

Subproblem 2

t + -1.444444445 = -1.519421593 Simplifying t + -1.444444445 = -1.519421593 Reorder the terms: -1.444444445 + t = -1.519421593 Solving -1.444444445 + t = -1.519421593 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.444444445' to each side of the equation. -1.444444445 + 1.444444445 + t = -1.519421593 + 1.444444445 Combine like terms: -1.444444445 + 1.444444445 = 0.000000000 0.000000000 + t = -1.519421593 + 1.444444445 t = -1.519421593 + 1.444444445 Combine like terms: -1.519421593 + 1.444444445 = -0.074977148 t = -0.074977148 Simplifying t = -0.074977148

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.963866038, -0.074977148}

See similar equations:

| 7d=-1 | | 3(2+3r)= | | -5(1-7v)=v-39 | | 4x+6=4x+5 | | -2000000+(80000x)=3600000 | | 11u=6u+84 | | 7x-12-(5x-4)=4(2x+3)-3 | | 2r+6r=88 | | -2(3x+8)=-18-76x | | -2000000+(-80000)x=3600000 | | 48000=x-x(.28) | | -2x-8=11 | | 45+1.99=68.88 | | -2000000+(80000)x=3600000 | | 3(2+5f)= | | 6.25=2x | | -18=3(-z+6)+27 | | (X^3-9X^2+15X+25)=0 | | 2(5+6m)= | | -8(1-4x)+5=-x-36 | | 4x^2+8x=4x | | 85-20x=60 | | 8x-4(2x+3)=5x-17 | | 8(r-5)= | | 3(1+t)= | | 3(2z+1)-4(z+2)= | | z^3+2+2i=0 | | 4+5(6x+8xy)+9yx= | | 14-(3x+2)=14-3x-2 | | 3x+3y+-3x+17y=180 | | 3(2x-5)=19-2(4x+5) | | -1.5a+6=-24 |

Equations solver categories