School Helper - Các bài tập gần đây đã giải quyết

solve the equation

Amanita, let's solve the equation $x^2 - 2x - 3 = 0$ by focusing on the "Completing the Square" method, as highlighted in the green rectangle. Here’s the step-by-step plan:

Step 1: Move the constant to the other side.
Start with the equation:

x^2 - 2x - 3 = 0

Add 3 to both sides:

x^2 - 2x = 3

Step 2: Complete the square.
To complete the square, take half of the coefficient of $x$ (which is $-2$ ), square it, and add it to both sides:

\left(\frac{-2}{2}\right)^2 = 1

Add 1 to both sides:

$x^2 - 2x + 1 = 3 + 1$

This gives:

(x-1)^2 = 4

Step 3: Solve for $x$ by taking the square root of both sides.

x-1 = \pm\sqrt{4}

x-1 = \pm2

Step 4: Solve for $x$ .
Add 1 to both sides for each case:

x = 1 + 2 = 3

x = 1 - 2 = -1

Now, let's confirm these solutions using a tool. Amanita, after following the steps for completing the square, we found the solutions to the equation $x^2 - 2x - 3 = 0$ are:

$x = 3 \quad \text{and} \quad x = -1$

This matches the results from the other methods shown in the image and confirms our answer is correct!