Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = -3 \)
Solution
สมการกำลังสอง: \( x^{2} + 6x + 9 = 0 \)
**ขั้นตอนการแก้สมการ:**
1. **ตรวจสอบว่าเป็นสมการกำลังสองสมบูรณ์ (Perfect Square Trinomial):**
สมการ \( x^{2} + 6x + 9 \) สามารถเขียนใหม่เป็นรูปกำลังสองสมบูรณ์ได้ดังนี้:
\[
(x + 3)^{2} = 0
\]
2. **แก้สมการสำหรับ \( x \):**
เนื่องจาก \( (x + 3)^{2} = 0 \) เราจึงมี:
\[
x + 3 = 0
\]
ดังนั้น:
\[
x = -3
\]
**คำตอบ:** \( x = -3 \)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
This equation is a perfect square trinomial, which can be factored as \( (x + 3)^2 = 0 \). This means that the solution to the equation is \( x = -3 \) with a multiplicity of 2, indicating that the graph of the related function touches the x-axis at this point but does not cross it. When solving quadratic equations like this, a common mistake is forgetting to check the discriminant. For \( ax^2 + bx + c = 0 \), you calculate the discriminant with \( D = b^2 - 4ac \). If \( D < 0 \), the equation has no real solutions, and if \( D = 0 \), it has one real solution (like in this case!). Always double-check to avoid overlooking these scenarios!
