-3x^2-30x+54=0

Simple and best practice solution for -3x^2-30x+54=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^2-30x+54=0 equation: 


Simplifying
-3x2 + -30x + 54 = 0

Reorder the terms:
54 + -30x + -3x2 = 0

Solving
54 + -30x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(18 + -10x + -1x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(18 + -10x + -1x2)' equal to zero and attempt to solve:

Simplifying
18 + -10x + -1x2 = 0

Solving
18 + -10x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-18 + 10x + x2 = 0

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 10x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + 10x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 10x + x2 = 0 + 18
10x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
10x + x2 = 18

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 18 + 25

Reorder the terms:
25 + 10x + x2 = 18 + 25

Combine like terms: 18 + 25 = 43
25 + 10x + x2 = 43

Factor a perfect square on the left side:
(x + 5)(x + 5) = 43

Calculate the square root of the right side: 6.557438524

Break this problem into two subproblems by setting 
(x + 5) equal to 6.557438524 and -6.557438524.


Subproblem 1
x + 5 = 6.557438524

Simplifying
x + 5 = 6.557438524

Reorder the terms:
5 + x = 6.557438524

Solving
5 + x = 6.557438524

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 6.557438524 + -5

Combine like terms: 5 + -5 = 0
0 + x = 6.557438524 + -5
x = 6.557438524 + -5

Combine like terms: 6.557438524 + -5 = 1.557438524
x = 1.557438524

Simplifying
x = 1.557438524


Subproblem 2
x + 5 = -6.557438524

Simplifying
x + 5 = -6.557438524

Reorder the terms:
5 + x = -6.557438524

Solving
5 + x = -6.557438524

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -6.557438524 + -5

Combine like terms: 5 + -5 = 0
0 + x = -6.557438524 + -5
x = -6.557438524 + -5

Combine like terms: -6.557438524 + -5 = -11.557438524
x = -11.557438524

Simplifying
x = -11.557438524


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.557438524, -11.557438524}
Solution
x = {1.557438524, -11.557438524}

See similar equations:

| 5m+9=2m+15 | | 5g=3 | | -14.5*-1.5y=-31 | | 0.8+0.5t=0.6 | | 4(x-2)-8(x+2)/3=5 | | 125000+(.90xQ)=230000+(.23xQ) | | 4(x-7)=2x+12 | | 4(x-7)=2x+12 | | 255(3.50x+150)=2000 | | 7e^2x=28e^6x | | z+9=-7 | | 13t+(-12t)=12t+(-12)t+3.14 | | 7a^2+a^2+16= | | 4(x-7)+2x+12=180 | | -4v-4+9v=51 | | 196x^2-6x+7=0 | | q+7=11 | | 150(3.50x+255)=2000 | | 13+19=4x | | 14/x=22/x-4 | | .75+x*2=7.5 | | 14/x=22/x-22 | | 3(x-7)=2(x-22) | | 3x-1+4x+3=8x-19 | | 0=-5x^4+20x^3+60x^2 | | 12+2m+2m+n+4n+3+2m+n+1+5m+n+2= | | 3[q-7]=27 | | 3(x+2)=2(4x) | | n/8-12*8=-1 | | 10x+11+5x+19=180 | | 10x+11+5x+19=180 | | 10x+11+5x+19=180 |

Equations solver categories