3t^2-8t=14

Simple and best practice solution for 3t^2-8t=14 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^2-8t=14 equation:


Simplifying
3t2 + -8t = 14

Reorder the terms:
-8t + 3t2 = 14

Solving
-8t + 3t2 = 14

Solving for variable 't'.

Reorder the terms:
-14 + -8t + 3t2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + -8t + 3t2 = 0

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

Divide each side by '3'.
-4.666666667 + -2.666666667t + t2 = 0

Move the constant term to the right:

Add '4.666666667' to each side of the equation.
-4.666666667 + -2.666666667t + 4.666666667 + t2 = 0 + 4.666666667

Reorder the terms:
-4.666666667 + 4.666666667 + -2.666666667t + t2 = 0 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + -2.666666667t + t2 = 0 + 4.666666667
-2.666666667t + t2 = 0 + 4.666666667

Combine like terms: 0 + 4.666666667 = 4.666666667
-2.666666667t + t2 = 4.666666667

The t term is -2.666666667t.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667t + 1.777777780 + t2 = 4.666666667 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667t + t2 = 4.666666667 + 1.777777780

Combine like terms: 4.666666667 + 1.777777780 = 6.444444447
1.777777780 + -2.666666667t + t2 = 6.444444447

Factor a perfect square on the left side:
(t + -1.333333334)(t + -1.333333334) = 6.444444447

Calculate the square root of the right side: 2.538591036

Break this problem into two subproblems by setting 
(t + -1.333333334) equal to 2.538591036 and -2.538591036.

Subproblem 1

t + -1.333333334 = 2.538591036 Simplifying t + -1.333333334 = 2.538591036 Reorder the terms: -1.333333334 + t = 2.538591036 Solving -1.333333334 + t = 2.538591036 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + t = 2.538591036 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + t = 2.538591036 + 1.333333334 t = 2.538591036 + 1.333333334 Combine like terms: 2.538591036 + 1.333333334 = 3.87192437 t = 3.87192437 Simplifying t = 3.87192437

Subproblem 2

t + -1.333333334 = -2.538591036 Simplifying t + -1.333333334 = -2.538591036 Reorder the terms: -1.333333334 + t = -2.538591036 Solving -1.333333334 + t = -2.538591036 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + t = -2.538591036 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + t = -2.538591036 + 1.333333334 t = -2.538591036 + 1.333333334 Combine like terms: -2.538591036 + 1.333333334 = -1.205257702 t = -1.205257702 Simplifying t = -1.205257702

Solution

The solution to the problem is based on the solutions from the subproblems. t = {3.87192437, -1.205257702}

See similar equations:

| 6*b=15 | | 8t=-6+9t | | (3x+2)(-x)= | | 4x+-2+11x+17=90 | | -3+8x^2-x+8+7x^2+2x= | | x^2+6x=775 | | 7(3-x)= | | 20=-3(2x+2)+7x | | 5(3x-1)=2(8x-4)-x+20 | | 8(8x+16)=-256 | | 2(1x-20)=40 | | (x-5)(-2)= | | 15+13t(84-t)=84 | | (3x-1)(2x+1)= | | 6-7x=6x-8x-19 | | 2x+3x=-15-10 | | 30-48w+12=-54 | | 5ax-5bx-4ay+4by=0 | | 22=(6)+w | | -11(1+5x)=-59-7x | | 20=3(2x+2)+7x | | 7(2e+1)=35 | | -3(6p+3)-2(4-14p)-3(4+3p)=0 | | 128v^2-98= | | 4=3x-6 | | 15-(2m+5)=2+2m-16 | | .9x-.5(X-4)=.4(X-5) | | -3x(x+4)-3x=24 | | (6x-1)(-4x)= | | x+y+45=180 | | y=-2(1)-10 | | 5(3x-2)=9x-10+8x |

Equations solver categories