A quadratic equation is shown below:

x2 − 14x + 41 = 0

Which of the following is the first correct step to write the above equation in the form (x − p)2 = q, where p and q are integers? (5 points)

A:Add 8 to both sides of the equation
B:Add 9 to both sides of the equation
C:Subtract 8 from both sides of the equation
D:Subtract 9 from both sides of the equation

Question

12-06-2016
Mathematics

contestada

A quadratic equation is shown below:

x2 − 14x + 41 = 0

Which of the following is the first correct step to write the above equation in the form (x − p)2 = q, where p and q are integers? (5 points)

A:Add 8 to both sides of the equation
B:Add 9 to both sides of the equation
C:Subtract 8 from both sides of the equation
D:Subtract 9 from both sides of the equation

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metchelle metchelle · Answer 1 · 2016-06-25T09:50:17+02:00

Since the desired equation is a perfect square binomial, it is necessary to obtain a constant term (in the case of the given equation, 41) that is also a perfect square. To determine the perfect square needed, take the coefficient of the second term (14x) and divide it by two, then square it. It should yield "49". To obtain 49 as the constant term, we have to add 8 to both sides of the equation. Among the choices, the correct answer is A.

abidemiokin abidemiokin · Answer 2 · 2022-05-25T11:47:59+02:00

The first correct step to write the above equation in the form id to subtract 49 from both sides of the equation

Vertex form of an equation

The standard vertex form of an equation is expressed as:

a(x − p)² = q

Given the quadratic equation x^2 − 14x + 49 = 0

The first step is to subtract the constant of the expression from both sides as shown:

Subtract 49 from both sides of the equation to have:

x^2 − 14x + 49 = 0

x^2 − 14x + 49 - 49= 0 - 49

x^2 - 14x = -49

Hence the first correct step to write the above equation in the form id to subtract 49 from both sides of the equation

Learn more on vertex form here: https://brainly.com/question/17987697

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