While solving \(x^2+24x+17=0\) by the completing-square method, which number is added to make \(x^2+24x\) a perfect square?
Answer and explanation
Correct answer: 144
The coefficient of \(x\) is 24, so its half is 12. To complete the square, we add the square of this half: \(\left(\frac{24}{2}\right)^2=12^2=144\). Therefore, 144 is added to both sides. Remember that 12 is the half of the coefficient, while 144 is the number added.
Frequently asked questions
What is the correct answer to this question?
144
Why is this the correct answer?
The coefficient of \(x\) is 24, so its half is 12. To complete the square, we add the square of this half: \(\left(\frac{24}{2}\right)^2=12^2=144\). Therefore, 144 is added to both sides. Remember that 12 is the half of the coefficient, while 144 is the number added.
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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