z^2-12z=-17

Simple and best practice solution for z^2-12z=-17 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=-17 equation:


Simplifying
z2 + -12z = -17

Reorder the terms:
-12z + z2 = -17

Solving
-12z + z2 = -17

Solving for variable 'z'.

Reorder the terms:
17 + -12z + z2 = -17 + 17

Combine like terms: -17 + 17 = 0
17 + -12z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + -12z + -17 + z2 = 0 + -17

Reorder the terms:
17 + -17 + -12z + z2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -12z + z2 = 0 + -17
-12z + z2 = 0 + -17

Combine like terms: 0 + -17 = -17
-12z + z2 = -17

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 = -17 + 36

Reorder the terms:
36 + -12z + z2 = -17 + 36

Combine like terms: -17 + 36 = 19
36 + -12z + z2 = 19

Factor a perfect square on the left side:
(z + -6)(z + -6) = 19

Calculate the square root of the right side: 4.358898944

Break this problem into two subproblems by setting 
(z + -6) equal to 4.358898944 and -4.358898944.

Subproblem 1

z + -6 = 4.358898944 Simplifying z + -6 = 4.358898944 Reorder the terms: -6 + z = 4.358898944 Solving -6 + z = 4.358898944 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 = 4.358898944 + 6 Combine like terms: -6 + 6 = 0 0 + z = 4.358898944 + 6 z = 4.358898944 + 6 Combine like terms: 4.358898944 + 6 = 10.358898944 z = 10.358898944 Simplifying z = 10.358898944

Subproblem 2

z + -6 = -4.358898944 Simplifying z + -6 = -4.358898944 Reorder the terms: -6 + z = -4.358898944 Solving -6 + z = -4.358898944 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 = -4.358898944 + 6 Combine like terms: -6 + 6 = 0 0 + z = -4.358898944 + 6 z = -4.358898944 + 6 Combine like terms: -4.358898944 + 6 = 1.641101056 z = 1.641101056 Simplifying z = 1.641101056

Solution

The solution to the problem is based on the solutions from the subproblems. z = {10.358898944, 1.641101056}

See similar equations:

| 2(5n+10)=40 | | 1/2(12-x)=20 | | y+6=.125(x-8) | | 2(x-4)+8=x-3(x+1) | | 2x+15=x+18 | | -7(10-4x)=-14 | | 1/18k=30 | | 5x^2+19x-8=0 | | 4x+4+x=6 | | 4(x-3)+7=10x-(x-3) | | (b-4)(b-6)= | | 7+6+x=5+8 | | 1/2(12-20)=x | | 6x+1=8x-3-5 | | 1/2(70-118)=x | | -ln(-2)+ln(-3)= | | y=5(2.1)x | | 1/2(80-118)=x | | 66=w/3 | | 1/29g=61 | | 6.1x-1.6=22.8 | | 2.1d+.07=7 | | 250=1432 | | X+[x+8]+[x+16]=888 | | 4(s+10)= | | (u+7)(u+3)= | | 2(x-4)=4x+3+6x | | Y+4=8(x+4) | | x+20=3x-32 | | 96=18x+x | | 2w^2-6w=12w-48 | | 252.3d=5802.9 |

Equations solver categories