Question #6446328Fill in the Blank
Algebra-1
Question
Solve the quadratic equation by completing the square. The solution is .
Answer & Analysis
Analysis
Question Analysis
This question tests the student's ability to solve a quadratic equation by completing the square. The equation given is in the form , and the student needs to complete the square to find the solutions.
This question tests the student's ability to solve a quadratic equation by completing the square. The equation given is in the form , and the student needs to complete the square to find the solutions.
Key Concept Explanation
Completing the square involves transforming the quadratic equation into a perfect square trinomial, which can then be solved by taking the square root of both sides.
Completing the square involves transforming the quadratic equation into a perfect square trinomial, which can then be solved by taking the square root of both sides.
Step-by-step Solution
1. Start with the equation .
2. Transpose the constant term to the right side: .
3. Complete the square: The coefficient of the linear term is 8, half of it is 4, and its square is 16.
Add 16 to both sides: , which simplifies to
1. Start with the equation .
2. Transpose the constant term to the right side: .
3. Complete the square: The coefficient of the linear term is 8, half of it is 4, and its square is 16.
Add 16 to both sides: , which simplifies to
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