6x^2+41x+29=0

Simple and best practice solution for 6x^2+41x+29=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+41x+29=0 equation: 


Simplifying
6x2 + 41x + 29 = 0

Reorder the terms:
29 + 41x + 6x2 = 0

Solving
29 + 41x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
4.833333333 + 6.833333333x + x2 = 0

Move the constant term to the right:

Add '-4.833333333' to each side of the equation.
4.833333333 + 6.833333333x + -4.833333333 + x2 = 0 + -4.833333333

Reorder the terms:
4.833333333 + -4.833333333 + 6.833333333x + x2 = 0 + -4.833333333

Combine like terms: 4.833333333 + -4.833333333 = 0.000000000
0.000000000 + 6.833333333x + x2 = 0 + -4.833333333
6.833333333x + x2 = 0 + -4.833333333

Combine like terms: 0 + -4.833333333 = -4.833333333
6.833333333x + x2 = -4.833333333

The x term is 6.833333333x.  Take half its coefficient (3.416666667).
Square it (11.67361111) and add it to both sides.

Add '11.67361111' to each side of the equation.
6.833333333x + 11.67361111 + x2 = -4.833333333 + 11.67361111

Reorder the terms:
11.67361111 + 6.833333333x + x2 = -4.833333333 + 11.67361111

Combine like terms: -4.833333333 + 11.67361111 = 6.840277777
11.67361111 + 6.833333333x + x2 = 6.840277777

Factor a perfect square on the left side:
(x + 3.416666667)(x + 3.416666667) = 6.840277777

Calculate the square root of the right side: 2.615392471

Break this problem into two subproblems by setting 
(x + 3.416666667) equal to 2.615392471 and -2.615392471.


Subproblem 1
x + 3.416666667 = 2.615392471

Simplifying
x + 3.416666667 = 2.615392471

Reorder the terms:
3.416666667 + x = 2.615392471

Solving
3.416666667 + x = 2.615392471

Solving for variable 'x'.

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

Add '-3.416666667' to each side of the equation.
3.416666667 + -3.416666667 + x = 2.615392471 + -3.416666667

Combine like terms: 3.416666667 + -3.416666667 = 0.000000000
0.000000000 + x = 2.615392471 + -3.416666667
x = 2.615392471 + -3.416666667

Combine like terms: 2.615392471 + -3.416666667 = -0.801274196
x = -0.801274196

Simplifying
x = -0.801274196


Subproblem 2
x + 3.416666667 = -2.615392471

Simplifying
x + 3.416666667 = -2.615392471

Reorder the terms:
3.416666667 + x = -2.615392471

Solving
3.416666667 + x = -2.615392471

Solving for variable 'x'.

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

Add '-3.416666667' to each side of the equation.
3.416666667 + -3.416666667 + x = -2.615392471 + -3.416666667

Combine like terms: 3.416666667 + -3.416666667 = 0.000000000
0.000000000 + x = -2.615392471 + -3.416666667
x = -2.615392471 + -3.416666667

Combine like terms: -2.615392471 + -3.416666667 = -6.032059138
x = -6.032059138

Simplifying
x = -6.032059138


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.801274196, -6.032059138}

See similar equations:

| 5c+40=154 | | 3z-4=5w+2 | | 21m^2-15=0 | | f(h)=140+5.5h | | 5=2s+4 | | 6ln(x)=1 | | 6(c-2)=7+5c | | 5s=436454643536346546546.837 | | 8x-7=7x+3 | | 98-7x=11x+18 | | -11a=-40 | | 5ay+3=4-2y | | 3z-6=5z-3z | | 21m^2-15m=0 | | 5xy+3=4-2y | | 5y=-3x-5 | | 2y=6x+8 | | 3=-81 | | 5t-t-6=3t-7 | | a-(-17)=-39 | | r-8.9=-2.5 | | -5=12+x | | O(80)=16p | | b=13-a | | 3m=5m-8 | | H^2-9=0 | | I(2)=12f | | 3c-2cd-8c+7d= | | 0.9(8x+16)=1.8-(x+2) | | 3Y-4x=12 | | 6(x+1)-(-4x-9)=9x | | -3p+7=5-(11p+7) |

Equations solver categories