Noah and Lin are each trying to solve the equation x² - 6x + 10 = 0. They know that the solutions to x² = - 1 are i and -i, but they are not sure how to use this information to solve for x in their equation. Here is Noah's work:
x² - 6x + 10 = 0
x² - 6x = -10
x² - 6x + 9 = -10 + 9
(x-3)² = -1

Show how Noah can finish his work using complex numbers.

The steps for Noah finishing his work have been shown below and the solution is;

x = 3 + i and x = 3 - i

Noah's work is;

x² - 6x + 10 = 0

x² - 6x = -10

x² - 6x + 9 = -10 + 9

(x - 3)² = -1

Now, the next step would be to take the square root of both sides to obtain;

x - 3 = √(-1)

Now, we are told that the solution to x² = -1 are i and -i. Now, x² = -1 can also be written as;

x = √(-1)

Thus, the solution to x = √(-1) is i and -i.

Thus;

x - 3 = i and x - 3 = -i

Thus;

x = 3 + i and x = 3 - i

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Solving the equation we get

Step-by-step explanation:

Noah's step to solve the equation are:

The next step is to take square root on both sides because:

Now, we know that:

So, Solving the equation we get

thats not a system of equations, that is a solution