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Determine the roots of the equation x² + 6x + 9 = 0. (2023)
Determine the roots of the equation x² + 6x + 9 = 0. (2023)
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Practice Questions
1 question
Q1
Determine the roots of the equation x² + 6x + 9 = 0. (2023)
-3
3
0
-6
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This is a perfect square: (x + 3)² = 0, hence the root is x = -3.
Questions & Step-by-step Solutions
1 item
Q
Q: Determine the roots of the equation x² + 6x + 9 = 0. (2023)
Solution:
This is a perfect square: (x + 3)² = 0, hence the root is x = -3.
Steps: 7
Show Steps
Step 1: Identify the equation you need to solve, which is x² + 6x + 9 = 0.
Step 2: Recognize that the equation can be factored. Look for two numbers that multiply to 9 (the last number) and add up to 6 (the middle number).
Step 3: The numbers 3 and 3 work because 3 * 3 = 9 and 3 + 3 = 6.
Step 4: Rewrite the equation using these numbers: (x + 3)(x + 3) = 0.
Step 5: This can be simplified to (x + 3)² = 0.
Step 6: To find the root, set (x + 3) equal to 0: x + 3 = 0.
Step 7: Solve for x by subtracting 3 from both sides: x = -3.
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