3z^2-8z-27=0

Simple and best practice solution for 3z^2-8z-27=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^2-8z-27=0 equation:


Simplifying
3z2 + -8z + -27 = 0

Reorder the terms:
-27 + -8z + 3z2 = 0

Solving
-27 + -8z + 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'.
-9 + -2.666666667z + z2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -2.666666667z + 9 + z2 = 0 + 9

Reorder the terms:
-9 + 9 + -2.666666667z + z2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2.666666667z + z2 = 0 + 9
-2.666666667z + z2 = 0 + 9

Combine like terms: 0 + 9 = 9
-2.666666667z + z2 = 9

The z term is -2.666666667z.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667z + 1.777777780 + z2 = 9 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667z + z2 = 9 + 1.777777780

Combine like terms: 9 + 1.777777780 = 10.77777778
1.777777780 + -2.666666667z + z2 = 10.77777778

Factor a perfect square on the left side:
(z + -1.333333334)(z + -1.333333334) = 10.77777778

Calculate the square root of the right side: 3.282952601

Break this problem into two subproblems by setting 
(z + -1.333333334) equal to 3.282952601 and -3.282952601.

Subproblem 1

z + -1.333333334 = 3.282952601 Simplifying z + -1.333333334 = 3.282952601 Reorder the terms: -1.333333334 + z = 3.282952601 Solving -1.333333334 + z = 3.282952601 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + z = 3.282952601 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + z = 3.282952601 + 1.333333334 z = 3.282952601 + 1.333333334 Combine like terms: 3.282952601 + 1.333333334 = 4.616285935 z = 4.616285935 Simplifying z = 4.616285935

Subproblem 2

z + -1.333333334 = -3.282952601 Simplifying z + -1.333333334 = -3.282952601 Reorder the terms: -1.333333334 + z = -3.282952601 Solving -1.333333334 + z = -3.282952601 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + z = -3.282952601 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + z = -3.282952601 + 1.333333334 z = -3.282952601 + 1.333333334 Combine like terms: -3.282952601 + 1.333333334 = -1.949619267 z = -1.949619267 Simplifying z = -1.949619267

Solution

The solution to the problem is based on the solutions from the subproblems. z = {4.616285935, -1.949619267}

See similar equations:

| 9p=2q-6 | | M/12-8=-3 | | 5(4y-3)+7=3(3y+4)+23 | | -5(15a-4b+6c)=x | | 10x-2m=8x+2m | | (3)(-21)= | | y=24-7 | | 11(x+6.50+3.80)=120.45 | | .05x=5700 | | 4(3y-5)=8+2(7y+1) | | 5(f-5)=2(f+4) | | 4c+5d=15 | | 5x=5700 | | 3w^2+5w-50=0 | | n+5-2=8 | | 2(3-8)-4=10 | | -3x^2+5x+11=0 | | 20=x-.4x | | 8c-d=-3 | | B/14=21. | | Z^3-6z^2+z-6=0 | | 15x^-5y^2/9x^4y^-3 | | 24x=-22x+10 | | 0=24x^2+2x+8 | | 3+5b=-42 | | (-2-3i)/7i | | X+35+2x-15+5x=180 | | 4z^3+8z^2=60z | | 5m+7=3m+3 | | f+3.3(f+6.7)=-53.85 | | 20w+45=-16 | | 7w/w^2t1 |

Equations solver categories