6x^2-12x-16=0

Simple and best practice solution for 6x^2-12x-16=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 6x^2-12x-16=0 equation: 


Simplifying
6x2 + -12x + -16 = 0

Reorder the terms:
-16 + -12x + 6x2 = 0

Solving
-16 + -12x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -6x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + -6x + 3x2)' equal to zero and attempt to solve:

Simplifying
-8 + -6x + 3x2 = 0

Solving
-8 + -6x + 3x2 = 0

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

Divide each side by '3'.
-2.666666667 + -2x + x2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + -2x + 2.666666667 + x2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + -2x + x2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + -2x + x2 = 0 + 2.666666667
-2x + x2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
-2x + x2 = 2.666666667

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 2.666666667 + 1

Reorder the terms:
1 + -2x + x2 = 2.666666667 + 1

Combine like terms: 2.666666667 + 1 = 3.666666667
1 + -2x + x2 = 3.666666667

Factor a perfect square on the left side:
(x + -1)(x + -1) = 3.666666667

Calculate the square root of the right side: 1.914854216

Break this problem into two subproblems by setting 
(x + -1) equal to 1.914854216 and -1.914854216.


Subproblem 1
x + -1 = 1.914854216

Simplifying
x + -1 = 1.914854216

Reorder the terms:
-1 + x = 1.914854216

Solving
-1 + x = 1.914854216

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.914854216 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.914854216 + 1
x = 1.914854216 + 1

Combine like terms: 1.914854216 + 1 = 2.914854216
x = 2.914854216

Simplifying
x = 2.914854216


Subproblem 2
x + -1 = -1.914854216

Simplifying
x + -1 = -1.914854216

Reorder the terms:
-1 + x = -1.914854216

Solving
-1 + x = -1.914854216

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.914854216 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.914854216 + 1
x = -1.914854216 + 1

Combine like terms: -1.914854216 + 1 = -0.914854216
x = -0.914854216

Simplifying
x = -0.914854216


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.914854216, -0.914854216}
Solution
x = {2.914854216, -0.914854216}

See similar equations:

| 13x-6=3-x | | 6(5-y)-4y=38 | | 8r+36= | | x=11k-4-5k-4 | | 6+7h=10h | | 3/4n-6=12 | | 8y=5x-3 | | -14-5x= | | -10=4x+20 | | -5(4+2m)=-7m-38 | | (x+5)(x^2+4)(3x^2-7)=0 | | 1+3x=-3+3x | | 18=(h+1)cm+6cm | | (x^2+2x+15)=0 | | -4+2p=-20 | | 3/25x5/3 | | 7a-15=20 | | X^2-24x+91=0 | | f(n)=n-2 | | 8y+4=2(3y+2) | | 2x-3yi=-2-6i | | 1-7k=-8-4k | | (2x-5)=(x+8) | | (2x+29)=(10x-27) | | 8p-1=3p+9 | | -3x+16=-11x+32 | | 1/9(5) | | 180-(3x+5)=(9x-17) | | (2x+11)+(2x+11)=(8x-14) | | 9(v+1)-3v=2(3v+4)-14 | | -19x+11+12x=-10x | | -4(2x-4)=60 |

Equations solver categories