Answer :
Answer:
D) (x - 7) feet
Step-by-step explanation:
Solving the Problem
Understanding the Problem
We're told the area of a square window, which is the squared value of its side length (s²).
We need to find the value of that side length. Usually we would take the square root, but the area is given as a quadratic. So, we must identify its factors (the binomials whose product equal to the given area).
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Calculating our Final Answer
Solution 1: Quadratic Formula
The quadratic formula can be used to find the solutions to any quadratic. These solutions can be plugged into a factor whose value equates to 0. Thus, we can build the quadratic's factor from of its solutions.
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]x=\dfrac{-(-14) \pm \sqrt{(-14)^2-4(1)(49)}}{2(1)}[/tex]
[tex]x=\dfrac{14 \pm \sqrt0}{2}[/tex]
[tex]x=7[/tex]
The only factor, from the answer choices, whose value equal 0 after x = 7 is plugged in is (x - 7).
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Solution 2: Perfect Trinomials
Knowing that the factors must be the same, since the window is a square, the given quadratic must be a perfect trinomial.
Recalling the factors of x² - 14x +49, our answer must be (x - 7).
