3z^2+11z+4=0

Simple and best practice solution for 3z^2+11z+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 3z^2+11z+4=0 equation:


Simplifying
3z2 + 11z + 4 = 0

Reorder the terms:
4 + 11z + 3z2 = 0

Solving
4 + 11z + 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'.
1.333333333 + 3.666666667z + z2 = 0

Move the constant term to the right:

Add '-1.333333333' to each side of the equation.
1.333333333 + 3.666666667z + -1.333333333 + z2 = 0 + -1.333333333

Reorder the terms:
1.333333333 + -1.333333333 + 3.666666667z + z2 = 0 + -1.333333333

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + 3.666666667z + z2 = 0 + -1.333333333
3.666666667z + z2 = 0 + -1.333333333

Combine like terms: 0 + -1.333333333 = -1.333333333
3.666666667z + z2 = -1.333333333

The z term is 3.666666667z.  Take half its coefficient (1.833333334).
Square it (3.361111114) and add it to both sides.

Add '3.361111114' to each side of the equation.
3.666666667z + 3.361111114 + z2 = -1.333333333 + 3.361111114

Reorder the terms:
3.361111114 + 3.666666667z + z2 = -1.333333333 + 3.361111114

Combine like terms: -1.333333333 + 3.361111114 = 2.027777781
3.361111114 + 3.666666667z + z2 = 2.027777781

Factor a perfect square on the left side:
(z + 1.833333334)(z + 1.833333334) = 2.027777781

Calculate the square root of the right side: 1.424000625

Break this problem into two subproblems by setting 
(z + 1.833333334) equal to 1.424000625 and -1.424000625.

Subproblem 1

z + 1.833333334 = 1.424000625 Simplifying z + 1.833333334 = 1.424000625 Reorder the terms: 1.833333334 + z = 1.424000625 Solving 1.833333334 + z = 1.424000625 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + z = 1.424000625 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + z = 1.424000625 + -1.833333334 z = 1.424000625 + -1.833333334 Combine like terms: 1.424000625 + -1.833333334 = -0.409332709 z = -0.409332709 Simplifying z = -0.409332709

Subproblem 2

z + 1.833333334 = -1.424000625 Simplifying z + 1.833333334 = -1.424000625 Reorder the terms: 1.833333334 + z = -1.424000625 Solving 1.833333334 + z = -1.424000625 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.833333334' to each side of the equation. 1.833333334 + -1.833333334 + z = -1.424000625 + -1.833333334 Combine like terms: 1.833333334 + -1.833333334 = 0.000000000 0.000000000 + z = -1.424000625 + -1.833333334 z = -1.424000625 + -1.833333334 Combine like terms: -1.424000625 + -1.833333334 = -3.257333959 z = -3.257333959 Simplifying z = -3.257333959

Solution

The solution to the problem is based on the solutions from the subproblems. z = {-0.409332709, -3.257333959}

See similar equations:

| 6x-8=14+2x | | 5(z+1)=4(z+4) | | -16+n-4-8n=-3n+n | | 6x+14y = 16 | | 3x+3y = 12 | | -6u+14=-8u+2 | | 4s-24=32 | | 2x-5+x=3x-8 | | 3x^(-3/2)=12 | | 40=.5h^2 | | 9/x=5/2 | | 3x^-3/2=12 | | 53=.5h^2 | | (4p+7)-(3p-1)= | | -3x+4=2x-20+x | | (x-4)(x-4)=225 | | 2x^2+24=-16x | | 3w-17=5w-5 | | 0=-16t^2-400 | | 4a/9a= | | x+7.5forx=2.5 | | Ln(36)-ln(2)=ln(x) | | 3+8forg=14 | | 15-5y=3 | | 3/x=70/28 | | 72m=3 | | (-8k^8)(-5k^3)= | | 12-2m=3 | | 17r=52 | | (360-x)-(x)=45 | | G+7=12 | | X^3-2x^2+1x=0 |

Equations solver categories