-6t^2+22t+21=0

Simple and best practice solution for -6t^2+22t+21=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 -6t^2+22t+21=0 equation:


Simplifying
-6t2 + 22t + 21 = 0

Reorder the terms:
21 + 22t + -6t2 = 0

Solving
21 + 22t + -6t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-3.5 + -3.666666667t + t2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -3.666666667t + 3.5 + t2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -3.666666667t + t2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -3.666666667t + t2 = 0 + 3.5
-3.666666667t + t2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-3.666666667t + t2 = 3.5

The t term is -3.666666667t.  Take half its coefficient (-1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
-3.666666667t + 3.361111114 + t2 = 3.5 + 3.361111114

Reorder the terms:
3.361111114 + -3.666666667t + t2 = 3.5 + 3.361111114

Combine like terms: 3.5 + 3.361111114 = 6.861111114
3.361111114 + -3.666666667t + t2 = 6.861111114

Factor a perfect square on the left side:
(t + -1.833333334)(t + -1.833333334) = 6.861111114

Calculate the square root of the right side: 2.619372275

Break this problem into two subproblems by setting 
(t + -1.833333334) equal to 2.619372275 and -2.619372275.

Subproblem 1

t + -1.833333334 = 2.619372275 Simplifying t + -1.833333334 = 2.619372275 Reorder the terms: -1.833333334 + t = 2.619372275 Solving -1.833333334 + t = 2.619372275 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + t = 2.619372275 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + t = 2.619372275 + 1.833333334 t = 2.619372275 + 1.833333334 Combine like terms: 2.619372275 + 1.833333334 = 4.452705609 t = 4.452705609 Simplifying t = 4.452705609

Subproblem 2

t + -1.833333334 = -2.619372275 Simplifying t + -1.833333334 = -2.619372275 Reorder the terms: -1.833333334 + t = -2.619372275 Solving -1.833333334 + t = -2.619372275 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.833333334' to each side of the equation. -1.833333334 + 1.833333334 + t = -2.619372275 + 1.833333334 Combine like terms: -1.833333334 + 1.833333334 = 0.000000000 0.000000000 + t = -2.619372275 + 1.833333334 t = -2.619372275 + 1.833333334 Combine like terms: -2.619372275 + 1.833333334 = -0.786038941 t = -0.786038941 Simplifying t = -0.786038941

Solution

The solution to the problem is based on the solutions from the subproblems. t = {4.452705609, -0.786038941}

See similar equations:

| r-9=13 | | 9y-6x-18=0 | | -20=-4p-12 | | 3x+(4x-5)=68 | | a+(-5)=8 | | -4-(3x)=(7x)-6 | | 31+5=44 | | 8+3h=15 | | 8h+18=42 | | -10n-4+9=4 | | 8b-66=62 | | 3n+4=52 | | 10n+4+9=4 | | (3x+1)=5(x-2) | | 5x^2+3x-8=2x^2-7x | | 3m-7=3m | | 8u-35=61 | | 43-5x=4x+24 | | 7r-20=43 | | 7x-3=9x+5 | | b+b+b= | | 3x+6=4x+16 | | h=-0.4x(x-80) | | 5x-1=21 | | x^2-6x-400=0 | | 6(4n+4)=8(3+3n) | | 10-10x=46-38x | | 7r-26=114 | | 3x+14=-10-9x | | 4q+1=81 | | 15-b=b | | 20x=15x+30 |

Equations solver categories