In the completing-the-square method, which number should be added and subtracted to solve the equation \(x^2+12x+7=0\)?
Answer and explanation
Correct answer: 36
In \(x^2+12x+7=0\), the coefficient of \(x\) is 12. To form a perfect square, calculate \(\left(\frac{12}{2}\right)^2=6^2=36\), so 36 is added and subtracted. Therefore, option A is correct. Exam tip: for \(x^2+bx\), use \(\left(\frac{b}{2}\right)^2\). Taking 12 or 6 alone does not complete the square.
Frequently asked questions
What is the correct answer to this question?
36
Why is this the correct answer?
In \(x^2+12x+7=0\), the coefficient of \(x\) is 12. To form a perfect square, calculate \(\left(\frac{12}{2}\right)^2=6^2=36\), so 36 is added and subtracted. Therefore, option A is correct. Exam tip: for \(x^2+bx\), use \(\left(\frac{b}{2}\right)^2\). Taking 12 or 6 alone does not 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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