9x^2+48x+27=0

Simple and best practice solution for 9x^2+48x+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 9x^2+48x+27=0 equation: 


Simplifying
9x2 + 48x + 27 = 0

Reorder the terms:
27 + 48x + 9x2 = 0

Solving
27 + 48x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + 16x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(9 + 16x + 3x2)' equal to zero and attempt to solve:

Simplifying
9 + 16x + 3x2 = 0

Solving
9 + 16x + 3x2 = 0

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

Divide each side by '3'.
3 + 5.333333333x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 5.333333333x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 5.333333333x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5.333333333x + x2 = 0 + -3
5.333333333x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
5.333333333x + x2 = -3

The x term is 5.333333333x.  Take half its coefficient (2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
5.333333333x + 7.111111113 + x2 = -3 + 7.111111113

Reorder the terms:
7.111111113 + 5.333333333x + x2 = -3 + 7.111111113

Combine like terms: -3 + 7.111111113 = 4.111111113
7.111111113 + 5.333333333x + x2 = 4.111111113

Factor a perfect square on the left side:
(x + 2.666666667)(x + 2.666666667) = 4.111111113

Calculate the square root of the right side: 2.027587511

Break this problem into two subproblems by setting 
(x + 2.666666667) equal to 2.027587511 and -2.027587511.


Subproblem 1
x + 2.666666667 = 2.027587511

Simplifying
x + 2.666666667 = 2.027587511

Reorder the terms:
2.666666667 + x = 2.027587511

Solving
2.666666667 + x = 2.027587511

Solving for variable 'x'.

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

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + x = 2.027587511 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + x = 2.027587511 + -2.666666667
x = 2.027587511 + -2.666666667

Combine like terms: 2.027587511 + -2.666666667 = -0.639079156
x = -0.639079156

Simplifying
x = -0.639079156


Subproblem 2
x + 2.666666667 = -2.027587511

Simplifying
x + 2.666666667 = -2.027587511

Reorder the terms:
2.666666667 + x = -2.027587511

Solving
2.666666667 + x = -2.027587511

Solving for variable 'x'.

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

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + x = -2.027587511 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + x = -2.027587511 + -2.666666667
x = -2.027587511 + -2.666666667

Combine like terms: -2.027587511 + -2.666666667 = -4.694254178
x = -4.694254178

Simplifying
x = -4.694254178


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.639079156, -4.694254178}
Solution
x = {-0.639079156, -4.694254178}

See similar equations:

| x^4+81i=0 | | 0.66c=-3(3c+1) | | 4+81i=0 | | -87+78= | | x^4+81i= | | 22(x-4)=900 | | 22+4x=900 | | 22x=90 | | 2(22)+2x=900 | | 7(1.2-k)=14k | | 5c-4-c+1=8c+2 | | 4x^2-17x+7=0 | | 15y+6=12y-17 | | 2x+(x)3= | | x*x=108 | | 5n-7=9 | | 2x+11=-9x | | 7500=10y+20x | | 5x-4=11x-55 | | 2x+35=5x+1 | | 3a+4b-4a+2b= | | -127=9x-1 | | (a-x)(a-x)=9-x^2 | | -3k+10=49 | | x^2-3xy+2y^2=7 | | 96-4x=32x+40 | | 7x-9x+6=-4 | | 61-6x=8x+18 | | 4x+11=91-7x | | 7g+4e+g-8e= | | 8x+8-6x=40 | | 7-3(3x+2)=4 |

Equations solver categories