Answer:
x^2 + 7x - 3 = 0
Step-by-step explanation:
I think you meant "width of the frame" from outside of frame to outside of mirror.
Let x represent the width of the frame.
Area of mirror is (3 ft)(4 ft) = 12 ft^2. Total area of mirror and frame is 15 ft^2. The 3 ft^2 difference is the area of the frame.
But you were asked to find a quadratic equation that would give you the "width" of the frame.
The "new" width would be 3 + x and the "new" height would be 4 + x.
Then the area of the mirror and frame together would be
A = (3 + x)(4 + x) = 15 ft^2, or
12 + 7x + x^2 = 15 ft^2, or
x^2 + 7x - 3 = 0. This is the desired quadratic equation.
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