What are the solutions of the equation: z² - 12z + 36 = 0?

Solution:

Given, the equation is z² - 12z + 36 = 0

We have to find the solutions of the equation.

On factorising z² - 12z + 36,

By splitting the middle term, we get

z² - 12z + 36 = z² - 6z - 6z + 36

= z(z - 6) - 6(z - 6)

= (z - 6)(z - 6)

= (z - 6)²

Now, z² - 12z + 36 = 0

(z - 6)² = 0

Taking square root,

z - 6 = 0

z = 6

Therefore, the solution is z = 6.

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What are the solutions of the equation: z² - 12z + 36 = 0?

Summary:

The solution of the equation: z² - 12z + 36 is z = 6.