3x^2+9x+4=0

Simple and best practice solution for 3x^2+9x+4=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+4=0 equation:


Simplifying
3x2 + 9x + 4 = 0

Reorder the terms:
4 + 9x + 3x2 = 0

Solving
4 + 9x + 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'.
1.333333333 + 3x + x2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + 3x + -1.333333333 + x2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + 3x + x2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + 3x + x2 = 0 + -1.333333333
3x + x2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
3x + x2 = -1.333333333

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 = -1.333333333 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -1.333333333 + 2.25

Combine like terms: -1.333333333 + 2.25 = 0.916666667
2.25 + 3x + x2 = 0.916666667

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 0.916666667

Calculate the square root of the right side: 0.957427108

Break this problem into two subproblems by setting 
(x + 1.5) equal to 0.957427108 and -0.957427108.

Subproblem 1

x + 1.5 = 0.957427108 Simplifying x + 1.5 = 0.957427108 Reorder the terms: 1.5 + x = 0.957427108 Solving 1.5 + x = 0.957427108 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 = 0.957427108 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 0.957427108 + -1.5 x = 0.957427108 + -1.5 Combine like terms: 0.957427108 + -1.5 = -0.542572892 x = -0.542572892 Simplifying x = -0.542572892

Subproblem 2

x + 1.5 = -0.957427108 Simplifying x + 1.5 = -0.957427108 Reorder the terms: 1.5 + x = -0.957427108 Solving 1.5 + x = -0.957427108 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 = -0.957427108 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -0.957427108 + -1.5 x = -0.957427108 + -1.5 Combine like terms: -0.957427108 + -1.5 = -2.457427108 x = -2.457427108 Simplifying x = -2.457427108

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.542572892, -2.457427108}

See similar equations:

| 8b-6(2b+1)=3b-1 | | -5-v=-3(v+5) | | 2x+y=4 | | 17x+5=180 | | 2(-7n+3)=-4(6+8n)-6n | | 6c=54 | | 3X+7=2X+10 | | -(-10p+2)=6p+8 | | m+15=20 | | 8=-5b-(9b+1) | | 4n+(3n+5)=47 | | 6x-1=13x-71 | | z-5=19 | | -4n+2-5=-3 | | -4=-(2+7a)-10a | | 55=5e | | x+23=-35 | | 6(5x+1)=2x-8x | | 378=18xz | | 71-6x=12x+15 | | 3(-2a+2)=9a-10 | | 13-10x=37-24x | | 3(-2+2)=9a-10 | | 2x+3x-12=4x-25 | | -127-8x=7x+23 | | 10+p=23 | | 3=10v-(-4v+1) | | k-13=18 | | 4x+6=-49-7x | | 3=10v-(4v+1) | | 75-3x=2x+15 | | 9+x=16 |

Equations solver categories