3t^2-7t-3=0

Simple and best practice solution for 3t^2-7t-3=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^2-7t-3=0 equation:


Simplifying
3t2 + -7t + -3 = 0

Reorder the terms:
-3 + -7t + 3t2 = 0

Solving
-3 + -7t + 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'.
-1 + -2.333333333t + t2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2.333333333t + 1 + t2 = 0 + 1

Reorder the terms:
-1 + 1 + -2.333333333t + t2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2.333333333t + t2 = 0 + 1
-2.333333333t + t2 = 0 + 1

Combine like terms: 0 + 1 = 1
-2.333333333t + t2 = 1

The t term is -2.333333333t.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333t + 1.361111112 + t2 = 1 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333t + t2 = 1 + 1.361111112

Combine like terms: 1 + 1.361111112 = 2.361111112
1.361111112 + -2.333333333t + t2 = 2.361111112

Factor a perfect square on the left side:
(t + -1.166666667)(t + -1.166666667) = 2.361111112

Calculate the square root of the right side: 1.536590743

Break this problem into two subproblems by setting 
(t + -1.166666667) equal to 1.536590743 and -1.536590743.

Subproblem 1

t + -1.166666667 = 1.536590743 Simplifying t + -1.166666667 = 1.536590743 Reorder the terms: -1.166666667 + t = 1.536590743 Solving -1.166666667 + t = 1.536590743 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + t = 1.536590743 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + t = 1.536590743 + 1.166666667 t = 1.536590743 + 1.166666667 Combine like terms: 1.536590743 + 1.166666667 = 2.70325741 t = 2.70325741 Simplifying t = 2.70325741

Subproblem 2

t + -1.166666667 = -1.536590743 Simplifying t + -1.166666667 = -1.536590743 Reorder the terms: -1.166666667 + t = -1.536590743 Solving -1.166666667 + t = -1.536590743 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + t = -1.536590743 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + t = -1.536590743 + 1.166666667 t = -1.536590743 + 1.166666667 Combine like terms: -1.536590743 + 1.166666667 = -0.369924076 t = -0.369924076 Simplifying t = -0.369924076

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.70325741, -0.369924076}

See similar equations:

| 6.6x-6+5x-1.8= | | -18t^2+45t^5=-9t^2 | | 150m+75m+52800=56100+200m | | 4-5b=8-6b | | 5x+19+8x-14=180 | | m-4m+5m+8= | | 8a^2-19a+15=0 | | 150m+75m+528000=56100+200m | | 10x^5-35x^3=5x^3 | | -5=-5t+5 | | 60x+15y=4740 | | m+3m-2m-4= | | 10x=12x+8 | | -3=p-6+6 | | 3v^2-2=5v | | .7t=1 | | 3+5a=7+3a | | -7-3x=x+13 | | 8k+12-11k-9= | | 310/395= | | -2m-13=-8m+27 | | 395/310= | | 0.75x-1.37=0.42-0.05 | | bx+a=ac | | -7c+12=-4c+78 | | 5/2*n=2 | | 10.25x-5.15=10.25x | | -4x(-4)+-8= | | (27x-49)(27x+49)= | | x=90+.9x | | 6+d=5d | | 6+d=-5d |

Equations solver categories