What is the standard form of the equation \(3(x+1)^2+2(x-4)^2=74\)?
Answer and explanation
Correct answer: 5x^2-10x-39=0
Expand the squares first: \(3(x+1)^2=3(x^2+2x+1)=3x^2+6x+3\) and \(2(x-4)^2=2(x^2-8x+16)=2x^2-16x+32\). Adding gives \(5x^2-10x+35=74\). Bring 74 to the left and simplify: \(5x^2-10x+35-74=0\), so \(5x^2-10x-39=0\). Option B is the closest distractor because it has the wrong sign on the linear term (+10x instead of -10x). Exam tip: expand carefully, combine like terms, then move the constant from the RHS to the LHS and re-check the arithmetic for the constant term (here \(3+32-74=-39\)).
Frequently asked questions
What is the correct answer to this question?
5x^2-10x-39=0
Why is this the correct answer?
Expand the squares first: \(3(x+1)^2=3(x^2+2x+1)=3x^2+6x+3\) and \(2(x-4)^2=2(x^2-8x+16)=2x^2-16x+32\). Adding gives \(5x^2-10x+35=74\). Bring 74 to the left and simplify: \(5x^2-10x+35-74=0\), so \(5x^2-10x-39=0\). Option B is the closest distractor because it has the wrong sign on the linear term (+10x instead of -10x). Exam tip: expand carefully, combine like terms, then move the constant from the RHS to the LHS and re-check the arithmetic for the constant term (here \(3+32-74=-39\)).
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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