3x^2-13x-40=0

Simple and best practice solution for 3x^2-13x-40=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 3x^2-13x-40=0 equation: 


Simplifying
3x2 + -13x + -40 = 0

Reorder the terms:
-40 + -13x + 3x2 = 0

Solving
-40 + -13x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-13.33333333 + -4.333333333x + x2 = 0

Move the constant term to the right:

Add '13.33333333' to each side of the equation.
-13.33333333 + -4.333333333x + 13.33333333 + x2 = 0 + 13.33333333

Reorder the terms:
-13.33333333 + 13.33333333 + -4.333333333x + x2 = 0 + 13.33333333

Combine like terms: -13.33333333 + 13.33333333 = 0.00000000
0.00000000 + -4.333333333x + x2 = 0 + 13.33333333
-4.333333333x + x2 = 0 + 13.33333333

Combine like terms: 0 + 13.33333333 = 13.33333333
-4.333333333x + x2 = 13.33333333

The x term is -4.333333333x.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333x + 4.694444446 + x2 = 13.33333333 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333x + x2 = 13.33333333 + 4.694444446

Combine like terms: 13.33333333 + 4.694444446 = 18.027777776
4.694444446 + -4.333333333x + x2 = 18.027777776

Factor a perfect square on the left side:
(x + -2.166666667)(x + -2.166666667) = 18.027777776

Calculate the square root of the right side: 4.245913067

Break this problem into two subproblems by setting 
(x + -2.166666667) equal to 4.245913067 and -4.245913067.


Subproblem 1
x + -2.166666667 = 4.245913067

Simplifying
x + -2.166666667 = 4.245913067

Reorder the terms:
-2.166666667 + x = 4.245913067

Solving
-2.166666667 + x = 4.245913067

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + x = 4.245913067 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = 4.245913067 + 2.166666667
x = 4.245913067 + 2.166666667

Combine like terms: 4.245913067 + 2.166666667 = 6.412579734
x = 6.412579734

Simplifying
x = 6.412579734


Subproblem 2
x + -2.166666667 = -4.245913067

Simplifying
x + -2.166666667 = -4.245913067

Reorder the terms:
-2.166666667 + x = -4.245913067

Solving
-2.166666667 + x = -4.245913067

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + x = -4.245913067 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = -4.245913067 + 2.166666667
x = -4.245913067 + 2.166666667

Combine like terms: -4.245913067 + 2.166666667 = -2.0792464
x = -2.0792464

Simplifying
x = -2.0792464


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.412579734, -2.0792464}

See similar equations:

| Y=60x+166 | | 6x(x)-10x=2 | | 14x=19y | | 2+t(-6t)-6=2 | | 12n^2-55n-25=0 | | 1.5=v+3/4 | | -12+6y+-1z=x | | 2+3=95 | | 4n-24=-31+5n | | 6y-4x=9 | | 4+5=241 | | 5s-14=18+9s | | 11^1/2 | | 3ln(6x)+2=14 | | 3(3+2x)-2=43 | | 6+(-6)= | | X^2+2X-200=0 | | ln(6x)=2 | | 361x^2+76x+2=0 | | 2x^2-1x-61=0 | | 2x+14=4x-12 | | x^2-10=10 | | x+4+2y=25 | | N=8800ln(7(2)+9) | | 84=v/3 | | 2x^2+8x-7=0 | | 3x^2+24x+42=0 | | x^2+-12x-12=0 | | 12a+7-2a-3= | | -15x^2-154x-25=0 | | 16v^3w^6+28v^5w^7y^2= | | 8t^2-4t^2= |

Equations solver categories