3x^2+27x+14=0

Simple and best practice solution for 3x^2+27x+14=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+27x+14=0 equation: 


Simplifying
3x2 + 27x + 14 = 0

Reorder the terms:
14 + 27x + 3x2 = 0

Solving
14 + 27x + 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'.
4.666666667 + 9x + x2 = 0

Move the constant term to the right:

Add '-4.666666667' to each side of the equation.
4.666666667 + 9x + -4.666666667 + x2 = 0 + -4.666666667

Reorder the terms:
4.666666667 + -4.666666667 + 9x + x2 = 0 + -4.666666667

Combine like terms: 4.666666667 + -4.666666667 = 0.000000000
0.000000000 + 9x + x2 = 0 + -4.666666667
9x + x2 = 0 + -4.666666667

Combine like terms: 0 + -4.666666667 = -4.666666667
9x + x2 = -4.666666667

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = -4.666666667 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -4.666666667 + 20.25

Combine like terms: -4.666666667 + 20.25 = 15.583333333
20.25 + 9x + x2 = 15.583333333

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 15.583333333

Calculate the square root of the right side: 3.947573094

Break this problem into two subproblems by setting 
(x + 4.5) equal to 3.947573094 and -3.947573094.


Subproblem 1
x + 4.5 = 3.947573094

Simplifying
x + 4.5 = 3.947573094

Reorder the terms:
4.5 + x = 3.947573094

Solving
4.5 + x = 3.947573094

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 3.947573094 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 3.947573094 + -4.5
x = 3.947573094 + -4.5

Combine like terms: 3.947573094 + -4.5 = -0.552426906
x = -0.552426906

Simplifying
x = -0.552426906


Subproblem 2
x + 4.5 = -3.947573094

Simplifying
x + 4.5 = -3.947573094

Reorder the terms:
4.5 + x = -3.947573094

Solving
4.5 + x = -3.947573094

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -3.947573094 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -3.947573094 + -4.5
x = -3.947573094 + -4.5

Combine like terms: -3.947573094 + -4.5 = -8.447573094
x = -8.447573094

Simplifying
x = -8.447573094


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.552426906, -8.447573094}

See similar equations:

| t-(-3)=0 | | (7*g^2*h)(3g*h^2)= | | 6y+8=6 | | -5x-y=2 | | 6x-2-x=-1-3(x-4) | | -30d+12=17d | | 47.04-5+9= | | 4x^2+136x+67=0 | | s-(-2)=3 | | x^3+3x^2-3x-1=0 | | 4(2x+1)=5x+3x | | 2000=-25p | | 5+(-8)-3=29 | | b(x)=x^4-2x^3-17x^2+4x+30 | | 12x-72=120 | | -26.5-a=22.0 | | 13x-65=-8-5 | | 7p+21p-14p=316-50 | | 1+16x=4(4x+2) | | 4(5+2x)-5=3(3+7) | | 2klm*7lm*4km= | | 3q+2q= | | 13(9c-1)-10=115c+13 | | -3y+12=2(3y-4)-16 | | 6y-12=-3-6y | | 3x^2=4a | | (2n-9)-5(-2.4+4)= | | 1.6v-1.2=-29.84 | | 3r+(-12)=-57 | | -4x=-6x-10 | | 4a=3b^2 | | 12x^2+6ax+2b=0 |

Equations solver categories