0=t^2+6t-9

Simple and best practice solution for 0=t^2+6t-9 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 0=t^2+6t-9 equation:


Simplifying
0 = t2 + 6t + -9

Reorder the terms:
0 = -9 + 6t + t2

Solving
0 = -9 + 6t + t2

Solving for variable 't'.

Combine like terms: 0 + 9 = 9
9 + -6t + -1t2 = -9 + 6t + t2 + 9 + -6t + -1t2

Reorder the terms:
9 + -6t + -1t2 = -9 + 9 + 6t + -6t + t2 + -1t2

Combine like terms: -9 + 9 = 0
9 + -6t + -1t2 = 0 + 6t + -6t + t2 + -1t2
9 + -6t + -1t2 = 6t + -6t + t2 + -1t2

Combine like terms: 6t + -6t = 0
9 + -6t + -1t2 = 0 + t2 + -1t2
9 + -6t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
9 + -6t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-9 + 6t + t2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 6t + 9 + t2 = 0 + 9

Reorder the terms:
-9 + 9 + 6t + t2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 6t + t2 = 0 + 9
6t + t2 = 0 + 9

Combine like terms: 0 + 9 = 9
6t + t2 = 9

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 = 9 + 9

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

Combine like terms: 9 + 9 = 18
9 + 6t + t2 = 18

Factor a perfect square on the left side:
(t + 3)(t + 3) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(t + 3) equal to 4.242640687 and -4.242640687.

Subproblem 1

t + 3 = 4.242640687 Simplifying t + 3 = 4.242640687 Reorder the terms: 3 + t = 4.242640687 Solving 3 + t = 4.242640687 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 = 4.242640687 + -3 Combine like terms: 3 + -3 = 0 0 + t = 4.242640687 + -3 t = 4.242640687 + -3 Combine like terms: 4.242640687 + -3 = 1.242640687 t = 1.242640687 Simplifying t = 1.242640687

Subproblem 2

t + 3 = -4.242640687 Simplifying t + 3 = -4.242640687 Reorder the terms: 3 + t = -4.242640687 Solving 3 + t = -4.242640687 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 = -4.242640687 + -3 Combine like terms: 3 + -3 = 0 0 + t = -4.242640687 + -3 t = -4.242640687 + -3 Combine like terms: -4.242640687 + -3 = -7.242640687 t = -7.242640687 Simplifying t = -7.242640687

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.242640687, -7.242640687}

See similar equations:

| 4c+5=4c+3 | | 10=lx-3l | | x^2-6x-11=-8 | | 18=3p+6 | | k-10=7 | | 0.35(16-x)+x=0.40(16) | | x+2x+(x+8)= | | -16t^2+20t+240=0 | | 7xa-11=31 | | 2x+y+3z=6 | | 3.7+t=9.45 | | 6x+15y=4 | | kx-x=k^2-1 | | m+13.9=-5.3 | | 8=3.14 | | 3x+2x-5=13-2(x+2) | | 0.35(17-x)+x=0.40(17) | | 5+2x+6=17 | | b=95+(15+8)w | | 14-2(3x+6)=3x-(2x-16) | | -4n-18=16 | | 44.91=9g+3.69 | | .15(10-x)+x=0.40(10) | | 45=d^2 | | 4t^2-5t-60=0 | | -35=-22-w | | 5x+20=9x-53 | | 49x^3-9x=0 | | 8x-8y=32 | | 2y-4(6)=-12 | | 0.5+3=x-2 | | 23=14-x |

Equations solver categories