2t^2-12t-9=0

Simple and best practice solution for 2t^2-12t-9=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 2t^2-12t-9=0 equation:


Simplifying
2t2 + -12t + -9 = 0

Reorder the terms:
-9 + -12t + 2t2 = 0

Solving
-9 + -12t + 2t2 = 0

Solving for variable 't'.

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

Divide each side by '2'.
-4.5 + -6t + t2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -6t + 4.5 + t2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -6t + t2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -6t + t2 = 0 + 4.5
-6t + t2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-6t + t2 = 4.5

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 = 4.5 + 9

Reorder the terms:
9 + -6t + t2 = 4.5 + 9

Combine like terms: 4.5 + 9 = 13.5
9 + -6t + t2 = 13.5

Factor a perfect square on the left side:
(t + -3)(t + -3) = 13.5

Calculate the square root of the right side: 3.674234614

Break this problem into two subproblems by setting 
(t + -3) equal to 3.674234614 and -3.674234614.

Subproblem 1

t + -3 = 3.674234614 Simplifying t + -3 = 3.674234614 Reorder the terms: -3 + t = 3.674234614 Solving -3 + t = 3.674234614 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 = 3.674234614 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.674234614 + 3 t = 3.674234614 + 3 Combine like terms: 3.674234614 + 3 = 6.674234614 t = 6.674234614 Simplifying t = 6.674234614

Subproblem 2

t + -3 = -3.674234614 Simplifying t + -3 = -3.674234614 Reorder the terms: -3 + t = -3.674234614 Solving -3 + t = -3.674234614 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 = -3.674234614 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.674234614 + 3 t = -3.674234614 + 3 Combine like terms: -3.674234614 + 3 = -0.674234614 t = -0.674234614 Simplifying t = -0.674234614

Solution

The solution to the problem is based on the solutions from the subproblems. t = {6.674234614, -0.674234614}

See similar equations:

| y=0.0x^2-x+1 | | 4(-3y+16)=-13 | | 3/2u-2/5=-u-4/5 | | 3(3x+8)-9=9x+15 | | x^2+30x+450=0 | | 2/7x+5/7=-3/7 | | 4x^2-x=663 | | 67+2.5c=92 | | 3(3x+1)-4x=13 | | 2x+6x=2x | | -2(t+8)=12 | | (6(y-3)/5)=-2y | | 3(4x+7)=5(2x-6)-x | | 3x^2-48x-24=39 | | 2.65+0.05x=20 | | 3i/1-2i | | (3y-8)/2=y+6 | | 16r^2-92r-160=0 | | 7+16y+4y^2=0 | | 2x-12=-4y | | 4/5+5/-2 | | 4r^2-23r-40=0 | | y=5(-1/4)+6 | | 2n(r-4)=5(r+-7) | | (x+5y-4z)-(x-6y+2z)= | | -28=12q-2 | | 20x+11=11x+15 | | (x+5y-4z)(x-6y+2z)= | | 6(1-7x)=-39+3x | | 8(7)+7y=56 | | 30+2.2222222x=100 | | 2x^2/3=98 |

Equations solver categories