How do you solve z( z - 2) = 2?

2 Answers
Apr 25, 2017

z=1+√3 or z=1−√3

Explanation:

Let's solve your equation step-by-step.
z(z−2)=2

Step 1: Simplify both sides of the equation.
z2−2z=2

Step 2: Subtract 2 from both sides.
z2−2z−2=2−2
z2−2z−2=0

Step 3: Use quadratic formula with a=1, b=-2, c=-2.

z=−b±√(b2−4ac)/"2a"

z=−(−2)±√((−2)2−4(1)(−2))/"2(1)"

z=(2±√12)/"2"

z=1+√3 or z=1−√3

source:https://www.mathpapa.com/algebra-calculator.html

hope this helps!

Apr 25, 2017

z=1+sqrt3

z=1-sqrt3

Explanation:

Order of operations.
Multiply first.

z( z - 2) = 2

z^2 - 2z= 2

z^2 - 2z-2= 0

Solve the quadratic equation with your preferred method.
I will use the quadratic formula.

z=(-b+-sqrt(b^2-4ac))/(2a)

z=(-(-2)+-sqrt((-2)^2-4(1)(-2)))/(2(1))

z=(2+-sqrt(4+8))/(2)

z=(2+-sqrt(12))/(2)

z=(2+-sqrt(4*3))/(2)

z=(2+-2sqrt(3))/(2)

z=(cancel2+-cancel2sqrt(3))/(cancel2)

z=1+-sqrt(3)

So,

z=1+sqrt3

z=1-sqrt3