0=x^2+6x+1

Simple and best practice solution for 0=x^2+6x+1 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=x^2+6x+1 equation: 


Simplifying
0 = x2 + 6x + 1

Reorder the terms:
0 = 1 + 6x + x2

Solving
0 = 1 + 6x + x2

Solving for variable 'x'.

Combine like terms: 0 + -1 = -1
-1 + -6x + -1x2 = 1 + 6x + x2 + -1 + -6x + -1x2

Reorder the terms:
-1 + -6x + -1x2 = 1 + -1 + 6x + -6x + x2 + -1x2

Combine like terms: 1 + -1 = 0
-1 + -6x + -1x2 = 0 + 6x + -6x + x2 + -1x2
-1 + -6x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
-1 + -6x + -1x2 = 0 + x2 + -1x2
-1 + -6x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1 + -6x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 6x + x2) = 0

Ignore the factor -1.

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

Simplifying
1 + 6x + x2 = 0

Solving
1 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 6x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 6x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 6x + x2 = 0 + -1
6x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
6x + x2 = -1

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -1 + 9

Reorder the terms:
9 + 6x + x2 = -1 + 9

Combine like terms: -1 + 9 = 8
9 + 6x + x2 = 8

Factor a perfect square on the left side:
(x + 3)(x + 3) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + 3) equal to 2.828427125 and -2.828427125.


Subproblem 1
x + 3 = 2.828427125

Simplifying
x + 3 = 2.828427125

Reorder the terms:
3 + x = 2.828427125

Solving
3 + x = 2.828427125

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 2.828427125 + -3

Combine like terms: 3 + -3 = 0
0 + x = 2.828427125 + -3
x = 2.828427125 + -3

Combine like terms: 2.828427125 + -3 = -0.171572875
x = -0.171572875

Simplifying
x = -0.171572875


Subproblem 2
x + 3 = -2.828427125

Simplifying
x + 3 = -2.828427125

Reorder the terms:
3 + x = -2.828427125

Solving
3 + x = -2.828427125

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -2.828427125 + -3

Combine like terms: 3 + -3 = 0
0 + x = -2.828427125 + -3
x = -2.828427125 + -3

Combine like terms: -2.828427125 + -3 = -5.828427125
x = -5.828427125

Simplifying
x = -5.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.171572875, -5.828427125}
Solution
x = {-0.171572875, -5.828427125}

See similar equations:

| 2/3x-7=5/6 | | 3(x+5)=2(x-5)+x | | 8-.5z=.25z-7 | | Logex=-1 | | 2x^2+2x+80=0 | | -7+-6=x | | -8(x-5)+8=48 | | 3(2f+4)=3(3f-6) | | factoring(7b+3)(4b-12)=0 | | 7/2x-1/2=27/2 | | 2x^2-66x=0 | | 18x^-11y^20/28x^6y^-11 | | 4(5z-1)-4(2+9)=7(z+1) | | 8(x-9)=4+9x | | 19m^6y/76x^3y^8 | | 3n+1=7n+5 | | 3(x-2)=2x+19 | | D(sin(15x))=0 | | 6x-4(-2x-5)=8 | | 0.005x+x=241139 | | n/4-7=10 | | X-5=25.08 | | 2x^(2/3)-11x^(1/3)-6=0 | | a^7/3a^2 | | 9x+3=7x+10 | | 5.5(x-4)=0.5x+26 | | 9y-3=18 | | s+8=14 | | 5(k-2)-6=3k-(2k-3) | | 4(x-2)-3=2(x+3)-7 | | .05x+x=241139 | | 6x^(2/3)-17x^(1/3)-3=0 |

Equations solver categories