If x² + 4x + 1 = 0, which form is obtained by completing the square?
Answer and explanation
Correct answer: (x + 2)² = 3
Begin by moving the constant term to the right: x² + 4x = −1. To complete the square, add (4/2)² = 2² = 4 to both sides. The left side becomes x² + 4x + 4 = (x+2)², while the right side becomes −1+4=3. Therefore the equivalent equation is (x+2)²=3, so option A is correct. Option B has the wrong sign inside the square and would create −4x. Option C adds an incorrect amount and has the wrong coefficient structure, while option D fails to account for the added 4 on the right. Adding the same quantity to both sides preserves equivalence.
Frequently asked questions
What is the correct answer to this question?
(x + 2)² = 3
Why is this the correct answer?
Begin by moving the constant term to the right: x² + 4x = −1. To complete the square, add (4/2)² = 2² = 4 to both sides. The left side becomes x² + 4x + 4 = (x+2)², while the right side becomes −1+4=3. Therefore the equivalent equation is (x+2)²=3, so option A is correct. Option B has the wrong sign inside the square and would create −4x. Option C adds an incorrect amount and has the wrong coefficient structure, while option D fails to account for the added 4 on the right. Adding the same quantity to both sides preserves equivalence.
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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