Question

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.​

Answer 1

Answer:

Solving the equation $x^2 - 6x + 10 = 0$ we get $x=3+i \ , \ x=3-i$

Step-by-step explanation:

Noah's step to solve the equation $x^2 - 6x + 10 = 0$ are:

$x^2 - 6x + 10 = 0\\x^2 - 6x = -10\\x^2 - 6x + 9 = -10 + 9\\(x-3)^2 = -1$

The next step is to take square root on both sides because: $\sqrt{x^2}=x$

$\sqrt{(x-3)^2}=\sqrt{-1} \\x-3=\pm\sqrt{-1} \\x=\pm(\sqrt{-1})+3$

Now, we know that: $\sqrt{-1}=i$

$x=\pm(i)+3\\x=3+i \ , \ x=3-i$

So, Solving the equation $x^2 - 6x + 10 = 0$ we get $x=3+i \ , \ x=3-i$