3x^2+15x+5=0

Simple and best practice solution for 3x^2+15x+5=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+15x+5=0 equation: 


Simplifying
3x2 + 15x + 5 = 0

Reorder the terms:
5 + 15x + 3x2 = 0

Solving
5 + 15x + 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'.
1.666666667 + 5x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + 5x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + 5x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + 5x + x2 = 0 + -1.666666667
5x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
5x + x2 = -1.666666667

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -1.666666667 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -1.666666667 + 6.25

Combine like terms: -1.666666667 + 6.25 = 4.583333333
6.25 + 5x + x2 = 4.583333333

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 4.583333333

Calculate the square root of the right side: 2.140872096

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.140872096 and -2.140872096.


Subproblem 1
x + 2.5 = 2.140872096

Simplifying
x + 2.5 = 2.140872096

Reorder the terms:
2.5 + x = 2.140872096

Solving
2.5 + x = 2.140872096

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 2.140872096 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 2.140872096 + -2.5
x = 2.140872096 + -2.5

Combine like terms: 2.140872096 + -2.5 = -0.359127904
x = -0.359127904

Simplifying
x = -0.359127904


Subproblem 2
x + 2.5 = -2.140872096

Simplifying
x + 2.5 = -2.140872096

Reorder the terms:
2.5 + x = -2.140872096

Solving
2.5 + x = -2.140872096

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -2.140872096 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -2.140872096 + -2.5
x = -2.140872096 + -2.5

Combine like terms: -2.140872096 + -2.5 = -4.640872096
x = -4.640872096

Simplifying
x = -4.640872096


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.359127904, -4.640872096}

See similar equations:

| 8+7p-1=9p+28-5p | | 4x-17=2x+11 | | r^2-15tw+5wr-3tr=0 | | 6-(-n)=-1 | | -3a-5a+a=11 | | 3x^2-4x=7 | | (7x^3-3x^2+2)-(2x^3+6x-9)= | | w=lvh | | 4x-16=2x+11 | | (s+4)(s-2)= | | 5+8x=6x | | -n+5=-12 | | n+2.5=0 | | 42-18x=19+5x | | x(3-2)+4(x-2)=43 | | 13r^2-117=0 | | 8+c=-3 | | x^4-7x^3+18x^2-20+6= | | 3y-9=-18 | | -4-x=-32 | | 3p^2+4p=10 | | (4x+4)(9x^2+5x+2)= | | 2(b+8)=48 | | n-(-13)=-54 | | 2(b+8)=-48 | | 3p^2+4p=0 | | 5m-10+36=-4 | | 2(b-8)=-48 | | 7(-3x-2)+4(1-x)=9(2x-5)-3(3x-5) | | -3+5x=-26 | | 3+1=5 | | 5x^2-30+46= |

Equations solver categories