3x^2+13x+3=0

Simple and best practice solution for 3x^2+13x+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+13x+3=0 equation:


Simplifying
3x2 + 13x + 3 = 0

Reorder the terms:
3 + 13x + 3x2 = 0

Solving
3 + 13x + 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 + 4.333333333x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 4.333333333x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 4.333333333x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4.333333333x + x2 = 0 + -1
4.333333333x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
4.333333333x + x2 = -1

The x term is 4.333333333x.  Take half its coefficient (2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
4.333333333x + 4.694444446 + x2 = -1 + 4.694444446

Reorder the terms:
4.694444446 + 4.333333333x + x2 = -1 + 4.694444446

Combine like terms: -1 + 4.694444446 = 3.694444446
4.694444446 + 4.333333333x + x2 = 3.694444446

Factor a perfect square on the left side:
(x + 2.166666667)(x + 2.166666667) = 3.694444446

Calculate the square root of the right side: 1.922093766

Break this problem into two subproblems by setting 
(x + 2.166666667) equal to 1.922093766 and -1.922093766.

Subproblem 1

x + 2.166666667 = 1.922093766 Simplifying x + 2.166666667 = 1.922093766 Reorder the terms: 2.166666667 + x = 1.922093766 Solving 2.166666667 + x = 1.922093766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = 1.922093766 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = 1.922093766 + -2.166666667 x = 1.922093766 + -2.166666667 Combine like terms: 1.922093766 + -2.166666667 = -0.244572901 x = -0.244572901 Simplifying x = -0.244572901

Subproblem 2

x + 2.166666667 = -1.922093766 Simplifying x + 2.166666667 = -1.922093766 Reorder the terms: 2.166666667 + x = -1.922093766 Solving 2.166666667 + x = -1.922093766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.166666667' to each side of the equation. 2.166666667 + -2.166666667 + x = -1.922093766 + -2.166666667 Combine like terms: 2.166666667 + -2.166666667 = 0.000000000 0.000000000 + x = -1.922093766 + -2.166666667 x = -1.922093766 + -2.166666667 Combine like terms: -1.922093766 + -2.166666667 = -4.088760433 x = -4.088760433 Simplifying x = -4.088760433

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.244572901, -4.088760433}

See similar equations:

| (3x-3)+(2x+5)+(4x-12)=89 | | -9v^2+35v-30=1-v | | 8x+1=4x+25 | | 4(2n-4)=(3n+6)+7 | | 5n+4n+5=23 | | 2x^2-17x=0 | | 2(w-1)+4=2-6w | | x^3-5x^2=0 | | (3x-3)+(2x+5)+(4x-12)= | | 0.6(x-2)=1.2 | | x^4-5x^2+16=0 | | =5a(-2ab^2)(-3b^3) | | 137+12x=-79+4x | | 18n^2+60n+50=0 | | 5x+3x-6x-5=1 | | -3(m-9)=2m-8 | | =5a(-2ab^2)(-3b^2) | | -7r^2+140r-700=0 | | 5y+2(y-8)=4(y+2)-2 | | x-4(2x+3)=23 | | =5m^4*3m^2 | | 5y+25=0 | | -4y^2+32y-64=0 | | 5m^4*3m^2= | | 2x^2-6=-78 | | -2w-16=2w | | 8a^2-72=0 | | 9(w-5)=-45 | | 120=6x+6(-4x-4) | | -3(t-4)+5y=4t-9 | | 6x+9=y | | -5=-(x+9) |

Equations solver categories