The area of a square is 7 more than 6 times its side. If the side is \(x\), which equation is correct?
Answer and explanation
Correct answer: \(x^2-6x-7=0\)
For a square with side \(x\), area = \(x^2\). The statement "7 more than 6 times its side" means area = \(6x+7\), so \(x^2=6x+7\). Rearranging gives \(x^2-6x-7=0\), which matches option A. The closest distractor C (\(x^2-7x-6=0\)) would correspond to area = \(7x+6\), which swaps the coefficients and is not what the question states. Option B has incorrect signs and option D has a different leading coefficient, so both are incorrect. Exam tip: Translate phrases like "a more than b times" as \(b x + a\) to avoid sign or order mistakes.
Frequently asked questions
What is the correct answer to this question?
\(x^2-6x-7=0\)
Why is this the correct answer?
For a square with side \(x\), area = \(x^2\). The statement "7 more than 6 times its side" means area = \(6x+7\), so \(x^2=6x+7\). Rearranging gives \(x^2-6x-7=0\), which matches option A. The closest distractor C (\(x^2-7x-6=0\)) would correspond to area = \(7x+6\), which swaps the coefficients and is not what the question states. Option B has incorrect signs and option D has a different leading coefficient, so both are incorrect. Exam tip: Translate phrases like "a more than b times" as \(b x + a\) to avoid sign or order mistakes.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Introduction to Quadratic Equations.
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