In the given equation \(x^2+8x=0\), what does \(x^2+8x+16\) become when a perfect square is formed by completing the square?
Answer and explanation
Correct answer: \((x+4)^2\)
In \(x^2+8x+16\), the coefficient of \(x\) is 8. Taking half of 8 gives 4, and adding its square, 16, gives \(x^2+8x+16=(x+4)^2\). Therefore, A is correct. In \((x+8)^2\), the middle term would be \(16x\), so B is incorrect. Exam tip: To complete the square in \(x^2+bx\), add \(\left(\frac{b}{2}\right)^2\).
Frequently asked questions
What is the correct answer to this question?
\((x+4)^2\)
Why is this the correct answer?
In \(x^2+8x+16\), the coefficient of \(x\) is 8. Taking half of 8 gives 4, and adding its square, 16, gives \(x^2+8x+16=(x+4)^2\). Therefore, A is correct. In \((x+8)^2\), the middle term would be \(16x\), so B is incorrect. Exam tip: To complete the square in \(x^2+bx\), add \(\left(\frac{b}{2}\right)^2\).
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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