z^2+12z-36=0

Simple and best practice solution for z^2+12z-36=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 z^2+12z-36=0 equation:


Simplifying
z2 + 12z + -36 = 0

Reorder the terms:
-36 + 12z + z2 = 0

Solving
-36 + 12z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 12z + 36 + z2 = 0 + 36

Reorder the terms:
-36 + 36 + 12z + z2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 12z + z2 = 0 + 36
12z + z2 = 0 + 36

Combine like terms: 0 + 36 = 36
12z + z2 = 36

The z term is 12z.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12z + 36 + z2 = 36 + 36

Reorder the terms:
36 + 12z + z2 = 36 + 36

Combine like terms: 36 + 36 = 72
36 + 12z + z2 = 72

Factor a perfect square on the left side:
(z + 6)(z + 6) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(z + 6) equal to 8.485281374 and -8.485281374.

Subproblem 1

z + 6 = 8.485281374 Simplifying z + 6 = 8.485281374 Reorder the terms: 6 + z = 8.485281374 Solving 6 + z = 8.485281374 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + z = 8.485281374 + -6 Combine like terms: 6 + -6 = 0 0 + z = 8.485281374 + -6 z = 8.485281374 + -6 Combine like terms: 8.485281374 + -6 = 2.485281374 z = 2.485281374 Simplifying z = 2.485281374

Subproblem 2

z + 6 = -8.485281374 Simplifying z + 6 = -8.485281374 Reorder the terms: 6 + z = -8.485281374 Solving 6 + z = -8.485281374 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + z = -8.485281374 + -6 Combine like terms: 6 + -6 = 0 0 + z = -8.485281374 + -6 z = -8.485281374 + -6 Combine like terms: -8.485281374 + -6 = -14.485281374 z = -14.485281374 Simplifying z = -14.485281374

Solution

The solution to the problem is based on the solutions from the subproblems. z = {2.485281374, -14.485281374}

See similar equations:

| 2(x+3)-7=5(5-x)+7(x+1) | | m^2(9m+6)=8m | | 2000=1000 | | y=6/7x+4 | | -1y-5/-9y | | 3z(5z+6)=15z^2+18z-1 | | 9r^3+18r^2=72 | | -8x+y=53 | | 9x+5y=-29 | | -8x+y=25 | | 8x+2y=-22 | | 9y^2-45y/-9y | | log(4)*(5x-3)=1 | | 3/x-2=70 | | (3i/4-i) | | (31/4-i) | | 3x^2+x=-5x | | x^2-7w=18 | | 3i/4-i | | 114/16x11 | | 3+9i/7+3i | | -4(4v-2x-1)= | | x^3=100y | | 2x-18+5x-5=180 | | (x^2-16)(6x+1)=0 | | x^2/6-5z/2-9=0 | | 2x^5-128x=0 | | 3i/4-1 | | 3x+33=8x-47 | | y=-2/3x-1/6 | | 242=(13+x)*17 | | -20+(-50)^2/60 |

Equations solver categories