3t^2+t-8=0

Simple and best practice solution for 3t^2+t-8=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+t-8=0 equation:


Simplifying
3t2 + t + -8 = 0

Reorder the terms:
-8 + t + 3t2 = 0

Solving
-8 + t + 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'.
-2.666666667 + 0.3333333333t + t2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + 0.3333333333t + 2.666666667 + t2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + 0.3333333333t + t2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + 0.3333333333t + t2 = 0 + 2.666666667
0.3333333333t + t2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
0.3333333333t + t2 = 2.666666667

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.3333333333t + 0.25 + t2 = 2.666666667 + 0.25

Reorder the terms:
0.25 + 0.3333333333t + t2 = 2.666666667 + 0.25

Combine like terms: 2.666666667 + 0.25 = 2.916666667
0.25 + 0.3333333333t + t2 = 2.916666667

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 2.916666667

Calculate the square root of the right side: 1.707825128

Break this problem into two subproblems by setting 
(t + 0.5) equal to 1.707825128 and -1.707825128.

Subproblem 1

t + 0.5 = 1.707825128 Simplifying t + 0.5 = 1.707825128 Reorder the terms: 0.5 + t = 1.707825128 Solving 0.5 + t = 1.707825128 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 1.707825128 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 1.707825128 + -0.5 t = 1.707825128 + -0.5 Combine like terms: 1.707825128 + -0.5 = 1.207825128 t = 1.207825128 Simplifying t = 1.207825128

Subproblem 2

t + 0.5 = -1.707825128 Simplifying t + 0.5 = -1.707825128 Reorder the terms: 0.5 + t = -1.707825128 Solving 0.5 + t = -1.707825128 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -1.707825128 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -1.707825128 + -0.5 t = -1.707825128 + -0.5 Combine like terms: -1.707825128 + -0.5 = -2.207825128 t = -2.207825128 Simplifying t = -2.207825128

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.207825128, -2.207825128}

See similar equations:

| 2=7/u-2 | | 9=4p | | 0.8=-2 | | 0.2-2=-4 | | 5x+9=1x+100 | | -4(x+2)-x+3=-5(x+2)+5 | | 5y^2+70y-75=0 | | (5x-2)= | | 3e11/3e6 | | (-(3/2)t | | 5x+17+12x-46=90 | | 32t^2+24t+80t+60=0 | | 6y-3=5y-4 | | -2(3x-4)=4(x-3) | | 15t^2-6t+4=0 | | 5n+2b=19.43 | | -11=x-(-3) | | Cos^2+3sen^2=0 | | 2(x-3)-4(x-1)+3(x-5)=x+20 | | 7-(2w+5)=-4+3(w+5) | | 2(3x-2)=3(2x+1) | | 7-(3w+5)=-4+3(w+5) | | 281=187-x | | y=7E-05 | | X+(7)=-1 | | f(x)=x^2-9x+4 | | (2/3)*(9/4) | | (3/8)/7 | | 4x-13x+3= | | 4x*2-13x+3= | | 3p-6=-26+8p | | 5/k?-6?=3 |

Equations solver categories