In the completing-square method for x² + 20x + 13 = 0, what number should be added and subtracted?
Answer and explanation
Correct answer: 100
The governing rule for completing the square is to add and subtract (b/2)² when the coefficient of x² is 1. In x² + 20x + 13 = 0, the coefficient b is 20. Half of 20 is 10, and squaring it gives 10² = 100. Therefore 100 must be both added and subtracted so that the first three terms can form a perfect square: x² + 20x + 100 = (x + 10)². The equation may then be written as (x + 10)² − 100 + 13 = 0, or (x + 10)² = 87. Hence option A is correct. The number 20 is the linear coefficient, 10 is only its half, and 13 is the constant term; none of these is the required added square.
Frequently asked questions
What is the correct answer to this question?
100
Why is this the correct answer?
The governing rule for completing the square is to add and subtract (b/2)² when the coefficient of x² is 1. In x² + 20x + 13 = 0, the coefficient b is 20. Half of 20 is 10, and squaring it gives 10² = 100. Therefore 100 must be both added and subtracted so that the first three terms can form a perfect square: x² + 20x + 100 = (x + 10)². The equation may then be written as (x + 10)² − 100 + 13 = 0, or (x + 10)² = 87. Hence option A is correct. The number 20 is the linear coefficient, 10 is only its half, and 13 is the constant term; none of these is the required added 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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