3z^2+12z+2=0

Simple and best practice solution for 3z^2+12z+2=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 3z^2+12z+2=0 equation:


Simplifying
3z2 + 12z + 2 = 0

Reorder the terms:
2 + 12z + 3z2 = 0

Solving
2 + 12z + 3z2 = 0

Solving for variable 'z'.

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

Divide each side by '3'.
0.6666666667 + 4z + z2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 4z + -0.6666666667 + z2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 4z + z2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 4z + z2 = 0 + -0.6666666667
4z + z2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
4z + z2 = -0.6666666667

The z term is 4z.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4z + 4 + z2 = -0.6666666667 + 4

Reorder the terms:
4 + 4z + z2 = -0.6666666667 + 4

Combine like terms: -0.6666666667 + 4 = 3.3333333333
4 + 4z + z2 = 3.3333333333

Factor a perfect square on the left side:
(z + 2)(z + 2) = 3.3333333333

Calculate the square root of the right side: 1.825741858

Break this problem into two subproblems by setting 
(z + 2) equal to 1.825741858 and -1.825741858.

Subproblem 1

z + 2 = 1.825741858 Simplifying z + 2 = 1.825741858 Reorder the terms: 2 + z = 1.825741858 Solving 2 + z = 1.825741858 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + z = 1.825741858 + -2 Combine like terms: 2 + -2 = 0 0 + z = 1.825741858 + -2 z = 1.825741858 + -2 Combine like terms: 1.825741858 + -2 = -0.174258142 z = -0.174258142 Simplifying z = -0.174258142

Subproblem 2

z + 2 = -1.825741858 Simplifying z + 2 = -1.825741858 Reorder the terms: 2 + z = -1.825741858 Solving 2 + z = -1.825741858 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + z = -1.825741858 + -2 Combine like terms: 2 + -2 = 0 0 + z = -1.825741858 + -2 z = -1.825741858 + -2 Combine like terms: -1.825741858 + -2 = -3.825741858 z = -3.825741858 Simplifying z = -3.825741858

Solution

The solution to the problem is based on the solutions from the subproblems. z = {-0.174258142, -3.825741858}

See similar equations:

| 3x-13=2x+45 | | 3x-13+2x+45=180 | | 5x+15-4x=-2-13 | | 5x+15-14x=-2-13 | | 3-13+2x+45=90 | | 61y=30(2y+10) | | 64x^2+2=0 | | 4-4=17x+8x | | x=-7+-2y | | 2x+45+3x-13=180 | | X-12=(16x)^1/2 | | ln(x)+ln(5)=0 | | 21-44=3(x-3)-5 | | 8(x-8)-6(x-5)+3x= | | 21-44=33(x-3)-5 | | 3x^2=17x+64 | | 2(8y-6)=4y | | 8x-20=4x-8 | | 3(x-1)+2(x+1)= | | -9-4=8x+5-7x | | 1x+4x=40 | | -870/x=-435 | | -870-x=-435 | | 5(3-2x)+x=3(2x+1)-8 | | 3(x+6)-1=7x+12 | | -435+x=-217.5 | | 0.6x^2+391x+0=0 | | 8x=6+6x | | -870+x=-435 | | 2x+6=3x-15 | | 1030/x=257.5 | | 325000= |

Equations solver categories