-6x^2-21x-3=0

Simple and best practice solution for -6x^2-21x-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 -6x^2-21x-3=0 equation: 


Simplifying
-6x2 + -21x + -3 = 0

Reorder the terms:
-3 + -21x + -6x2 = 0

Solving
-3 + -21x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-3'.
-3(1 + 7x + 2x2) = 0

Ignore the factor -3.

Subproblem 1
Set the factor '(1 + 7x + 2x2)' equal to zero and attempt to solve:

Simplifying
1 + 7x + 2x2 = 0

Solving
1 + 7x + 2x2 = 0

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

Divide each side by '2'.
0.5 + 3.5x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 3.5x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 3.5x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 3.5x + x2 = 0 + -0.5
3.5x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
3.5x + x2 = -0.5

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = -0.5 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = -0.5 + 3.0625

Combine like terms: -0.5 + 3.0625 = 2.5625
3.0625 + 3.5x + x2 = 2.5625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(x + 1.75) equal to 1.600781059 and -1.600781059.


Subproblem 1
x + 1.75 = 1.600781059

Simplifying
x + 1.75 = 1.600781059

Reorder the terms:
1.75 + x = 1.600781059

Solving
1.75 + x = 1.600781059

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 1.600781059 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 1.600781059 + -1.75
x = 1.600781059 + -1.75

Combine like terms: 1.600781059 + -1.75 = -0.149218941
x = -0.149218941

Simplifying
x = -0.149218941


Subproblem 2
x + 1.75 = -1.600781059

Simplifying
x + 1.75 = -1.600781059

Reorder the terms:
1.75 + x = -1.600781059

Solving
1.75 + x = -1.600781059

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -1.600781059 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -1.600781059 + -1.75
x = -1.600781059 + -1.75

Combine like terms: -1.600781059 + -1.75 = -3.350781059
x = -3.350781059

Simplifying
x = -3.350781059


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.149218941, -3.350781059}
Solution
x = {-0.149218941, -3.350781059}

See similar equations:

| -w^2+5w=3 | | 3(5-x)-4(3+2x)+2(12-17x)=0 | | 6x^2-21x-3=o | | 5x^3=20x | | 10(j+19)=80 | | .3=(50-x)/50 | | 3x^2-21x-3=0 | | .3=(x-50)/50 | | (x-1)(x-2)=0 | | 10-(-10)= | | 8n^2-8=0 | | X+Y=3x^420 | | 35=-3.5x | | z(3z-4)(z+3)=0 | | 24=(-v)/(-3) | | 4X-2=-X+3 | | 2m=2y | | 6(m-83)+7=55 | | 2.1x-3.24=1.26-5.4x | | (x-9)(x+1)(x-1)=0 | | X-4=-2X-7 | | 2p-11=-8(2-7p)+5 | | 24=-(v)/(3) | | 6r^3+30r^2=36r | | 2x+(4*7)=13 | | 3X-6=-X+2 | | (-a)/(10)-8=-24 | | 5-x=10 | | (2x-5)(3x+1)=0 | | (-x)/(3)+4=20 | | w^2-2w=35 | | 6t^2=34t-20 |

Equations solver categories