3t^2-18t+11=0

Simple and best practice solution for 3t^2-18t+11=0 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 3t^2-18t+11=0 equation:


Simplifying
3t2 + -18t + 11 = 0

Reorder the terms:
11 + -18t + 3t2 = 0

Solving
11 + -18t + 3t2 = 0

Solving for variable 't'.

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

Divide each side by '3'.
3.666666667 + -6t + t2 = 0

Move the constant term to the right:

Add '-3.666666667' to each side of the equation.
3.666666667 + -6t + -3.666666667 + t2 = 0 + -3.666666667

Reorder the terms:
3.666666667 + -3.666666667 + -6t + t2 = 0 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + -6t + t2 = 0 + -3.666666667
-6t + t2 = 0 + -3.666666667

Combine like terms: 0 + -3.666666667 = -3.666666667
-6t + t2 = -3.666666667

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = -3.666666667 + 9

Reorder the terms:
9 + -6t + t2 = -3.666666667 + 9

Combine like terms: -3.666666667 + 9 = 5.333333333
9 + -6t + t2 = 5.333333333

Factor a perfect square on the left side:
(t + -3)(t + -3) = 5.333333333

Calculate the square root of the right side: 2.309401077

Break this problem into two subproblems by setting 
(t + -3) equal to 2.309401077 and -2.309401077.

Subproblem 1

t + -3 = 2.309401077 Simplifying t + -3 = 2.309401077 Reorder the terms: -3 + t = 2.309401077 Solving -3 + t = 2.309401077 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 2.309401077 + 3 Combine like terms: -3 + 3 = 0 0 + t = 2.309401077 + 3 t = 2.309401077 + 3 Combine like terms: 2.309401077 + 3 = 5.309401077 t = 5.309401077 Simplifying t = 5.309401077

Subproblem 2

t + -3 = -2.309401077 Simplifying t + -3 = -2.309401077 Reorder the terms: -3 + t = -2.309401077 Solving -3 + t = -2.309401077 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -2.309401077 + 3 Combine like terms: -3 + 3 = 0 0 + t = -2.309401077 + 3 t = -2.309401077 + 3 Combine like terms: -2.309401077 + 3 = 0.690598923 t = 0.690598923 Simplifying t = 0.690598923

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.309401077, 0.690598923}

See similar equations:

| 2x^4-9x^3+9x^2+3x+13=0 | | 36/24=16/x | | 15/x=18/20 | | 3t^2-20t+16=0 | | 12-3y/2= | | 202/1000 | | 5x-6y=-51 | | -1/3*15-6=-11 | | -3.79=n+13.4 | | -1/3*15-6 | | 10*1.47/3.5 | | N+n+(n-8)=42 | | x-[4-2x]=7[x-1] | | 1.47/3.5 | | -7/9*3 | | 4x-9x+3=x-8+11 | | w+2.8=7.65 | | 64000/8000 | | 64/0.8 | | 0.64/0.008 | | 4y=1x-11 | | n+80=964 | | d-139=766 | | 250=124-3*x | | 8x-2=-3x-7 | | g+31=580 | | (18x-8)+(4x+6)= | | 6y-15.4=-4.3y+26.3 | | f(1)=-12x^2+72x-60 | | 73.15/0.05 | | 2ab+3ba=5ab | | f(x)=-12x^2+72x-60 |

Equations solver categories