3x^2-2x-27=0

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


Simplifying
3x2 + -2x + -27 = 0

Reorder the terms:
-27 + -2x + 3x2 = 0

Solving
-27 + -2x + 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'.
-9 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -0.6666666667x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -0.6666666667x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -0.6666666667x + x2 = 0 + 9
-0.6666666667x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-0.6666666667x + x2 = 9

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 9 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 9 + 0.1111111112

Combine like terms: 9 + 0.1111111112 = 9.1111111112
0.1111111112 + -0.6666666667x + x2 = 9.1111111112

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 9.1111111112

Calculate the square root of the right side: 3.018461713

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 3.018461713 and -3.018461713.


Subproblem 1
x + -0.3333333334 = 3.018461713

Simplifying
x + -0.3333333334 = 3.018461713

Reorder the terms:
-0.3333333334 + x = 3.018461713

Solving
-0.3333333334 + x = 3.018461713

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = 3.018461713 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 3.018461713 + 0.3333333334
x = 3.018461713 + 0.3333333334

Combine like terms: 3.018461713 + 0.3333333334 = 3.3517950464
x = 3.3517950464

Simplifying
x = 3.3517950464


Subproblem 2
x + -0.3333333334 = -3.018461713

Simplifying
x + -0.3333333334 = -3.018461713

Reorder the terms:
-0.3333333334 + x = -3.018461713

Solving
-0.3333333334 + x = -3.018461713

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = -3.018461713 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -3.018461713 + 0.3333333334
x = -3.018461713 + 0.3333333334

Combine like terms: -3.018461713 + 0.3333333334 = -2.6851283796
x = -2.6851283796

Simplifying
x = -2.6851283796


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.3517950464, -2.6851283796}

See similar equations:

| .6=-x+1 | | 3=15x-12 | | 55=7s+1-2s | | 5x^2-54=0 | | 113-4x=2x+23 | | 2+3(x+1)=6x | | 1.5+2x=6.5 | | 2x^2=-3x+2 | | 55501890= | | Q=50 | | Q= | | x^2+17x+29=0 | | x^2+17+29=0 | | 1-(x-3)=3(2x+1) | | -5(4b+1)+(21b-3)=0 | | 8g^2-14g+3=0 | | 2x-(1+3m)x+15m=0 | | x^2-7x+12.25=0 | | x-9-8x=27-10x | | x-4+(2x-1)=x-2 | | 3000-32+24=0 | | x-14+(2x-1)=x-2 | | 3x-32+24=0 | | 7p+5(p-q)-q= | | (-1/4)(4)(4)(4)(4)(4)= | | (-1/4)(4)(4)(4)(4)= | | 6x+12-4x=9x-16 | | 5w+6+-0.80w=27 | | (-1/4)(-1/4)(-1/4)(-1/4)= | | 10x+40=-25-3x | | 7-[7(3-6)-6]= | | 12x-13=2x+26 |

Equations solver categories