What is the standard form of the equation \\(2x-3\\)^2+(x+5)^2=34?
Answer and explanation
Correct answer: \\(5x^2-2x=0\\)
Expand the squares: \\( (2x-3)^2=4x^2-12x+9 \\) and \\( (x+5)^2=x^2+10x+25 \\). This gives \\(5x^2-2x+34=34\\); subtracting 34 from both sides yields \\(5x^2-2x=0\\). This matches the standard quadratic form \\(ax^2+bx+c=0\\), with \\(c=0\\). Exam tip: after expansion, bring all terms to one side and equate the result to zero.
Frequently asked questions
What is the correct answer to this question?
\\(5x^2-2x=0\\)
Why is this the correct answer?
Expand the squares: \\( (2x-3)^2=4x^2-12x+9 \\) and \\( (x+5)^2=x^2+10x+25 \\). This gives \\(5x^2-2x+34=34\\); subtracting 34 from both sides yields \\(5x^2-2x=0\\). This matches the standard quadratic form \\(ax^2+bx+c=0\\), with \\(c=0\\). Exam tip: after expansion, bring all terms to one side and equate the result to zero.
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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