When solving the equation \(x^2+16x+11=0\) by completing the square, which number must be added to both sides to make \(x^2+16x\) a perfect square?
Answer and explanation
Correct answer: 64
The coefficient of \(x\) is 16. Its half is 8, and the square of 8 is \(8^2=64\). Thus, adding 64 to both sides gives \(x^2+16x+64=(x+8)^2\). The number 8 is only half the coefficient, not the number to be added. Exam tip: For \(x^2+bx\), add \(\left(\frac{b}{2}\right)^2\) to complete the square.
Frequently asked questions
What is the correct answer to this question?
64
Why is this the correct answer?
The coefficient of \(x\) is 16. Its half is 8, and the square of 8 is \(8^2=64\). Thus, adding 64 to both sides gives \(x^2+16x+64=(x+8)^2\). The number 8 is only half the coefficient, not the number to be added. Exam tip: For \(x^2+bx\), add \(\left(\frac{b}{2}\right)^2\) to complete 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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