Solve a quadratic equation using square roots

Key Notes :

Understanding the Square Root Method

• The square root method is a technique for solving quadratic equations that are in the form:
  • ax² = k
  • (x-h)² = k
• This method is especially useful when the quadratic equation doesn’t have a linear term (bx).

Steps to Solve Using Square Roots

1. Isolate the x² Term: Ensure the quadratic equation is in the form where the x² term is alone on one side.
2. Apply the Square Root: Take the square root of both sides of the equation. Remember to consider both the positive and negative square roots.
3. Solve for x: Simplify the square root (if possible) and solve for x.

Special Cases

• No Real Solutions: If k is negative, there are no real solutions.
• Zero Solution: If k is zero, the only solution is x = 0.

Example

Solve: x² = 25

• Step 1: x² = 25 (already isolated)
• Step 2: x = ±√25
• Step 3: x = ±5

Key Points

• The square root method is a direct and efficient way to solve certain quadratic equations.
• It’s applicable when the equation can be expressed in the form of a perfect square.
• Always consider both the positive and negative square roots.
• Be aware of special cases where there might be no real solutions or a single solution.

Learn with an example

let’s practice!