Which step is correct while solving x² + 6x + 1 = 0 by completing the square?
Answer and explanation
Correct answer: (x + 3)² = 8
Completing the square means transforming the quadratic expression into a perfect-square expression without changing the equation. Start with x² + 6x + 1 = 0 and move the constant term: x² + 6x = −1. Half of the coefficient of x is 6/2 = 3, and its square is 9. Add 9 to both sides: x² + 6x + 9 = −1 + 9 = 8. The left side becomes (x + 3)², so (x + 3)² = 8. Therefore option A is correct. Option B uses the full coefficient instead of half, option C has an incorrect right side, and option D has the wrong sign inside the square.
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What is the correct answer to this question?
(x + 3)² = 8
Why is this the correct answer?
Completing the square means transforming the quadratic expression into a perfect-square expression without changing the equation. Start with x² + 6x + 1 = 0 and move the constant term: x² + 6x = −1. Half of the coefficient of x is 6/2 = 3, and its square is 9. Add 9 to both sides: x² + 6x + 9 = −1 + 9 = 8. The left side becomes (x + 3)², so (x + 3)² = 8. Therefore option A is correct. Option B uses the full coefficient instead of half, option C has an incorrect right side, and option D has the wrong sign inside the square.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Methods of Solving Quadratic Equations.
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