3x^2+9x+3=0

Simple and best practice solution for 3x^2+9x+3=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+9x+3=0 equation:


Simplifying
3x2 + 9x + 3 = 0

Reorder the terms:
3 + 9x + 3x2 = 0

Solving
3 + 9x + 3x2 = 0

Solving for variable 'x'.

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

Ignore the factor 3.

Subproblem 1

Set the factor '(1 + 3x + x2)' equal to zero and attempt to solve: Simplifying 1 + 3x + x2 = 0 Solving 1 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 3x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 3x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x + x2 = 0 + -1 3x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 3x + x2 = -1 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -1 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -1 + 2.25 Combine like terms: -1 + 2.25 = 1.25 2.25 + 3x + x2 = 1.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + 1.5) equal to 1.118033989 and -1.118033989.

Subproblem 1

x + 1.5 = 1.118033989 Simplifying x + 1.5 = 1.118033989 Reorder the terms: 1.5 + x = 1.118033989 Solving 1.5 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.118033989 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.118033989 + -1.5 x = 1.118033989 + -1.5 Combine like terms: 1.118033989 + -1.5 = -0.381966011 x = -0.381966011 Simplifying x = -0.381966011

Subproblem 2

x + 1.5 = -1.118033989 Simplifying x + 1.5 = -1.118033989 Reorder the terms: 1.5 + x = -1.118033989 Solving 1.5 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.118033989 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.118033989 + -1.5 x = -1.118033989 + -1.5 Combine like terms: -1.118033989 + -1.5 = -2.618033989 x = -2.618033989 Simplifying x = -2.618033989

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.381966011, -2.618033989}

Solution

x = {-0.381966011, -2.618033989}

See similar equations:

| 2n+5=n+8 | | 5-7x=35-21x | | -2X-10=-10 | | 13-7x=127-8x | | -2X-10=-4 | | x-8x^1/2+11=0 | | 20(t)=-4.9t^2+32t+2 | | 5y=18+2y | | w=675624782 | | 2x+20=9x+50 | | 12x=3x | | 256-2x=43x+16 | | 234-4x=41x+19 | | 2x+20=9+50 | | 3x-3=12x-91 | | 10y-9y=15 | | 10y-9y= | | 24-2y=6 | | (n+6)*7=14 | | (n+6)*2=4 | | (n+3)*3=15 | | 0=1.5x^2-9x+1080 | | 2w-7=w+1 | | 3344=3-250-453 | | h=J+K+5 | | l=j+k+t | | 8m=8 | | a=2b-c | | x^2-x-4=5 | | 2x^2+15x=3 | | (4x)*x=100 | | (4x)x(x)=100 |

Equations solver categories