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When solving the equation \(x^2-10x+7=0\) by completing the square method, which number should be added to make \(x^2-10x\) a perfect square?
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Answer and explanation
Correct answer: 25
The coefficient of \(x\) is \(-10\), whose half is \(-5\). Squaring it gives \((-5)^2=25\), so 25 must be added: \(x^2-10x+25=(x-5)^2\). Exam tip: in the completing-square method, add the square of half the coefficient of \(x\).
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What is the correct answer to this question?
25
Why is this the correct answer?
The coefficient of \(x\) is \(-10\), whose half is \(-5\). Squaring it gives \((-5)^2=25\), so 25 must be added: \(x^2-10x+25=(x-5)^2\). Exam tip: in the completing-square method, add the square of half the coefficient of \(x\).
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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