Carmen is using the quadratic equation (x + 15)(x) = 100 where x represents the width of a picture frame. Which statement about

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1 month ago

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Carmen is using the quadratic equation (x + 15)(x) = 100 where x represents the width of a picture frame. Which statement about

the solutions x = 5 and x = –20 is true? A. The solutions x = 5 and x = –20 are reasonable. B. The solution x = 5 should be kept, but x = –20 is unreasonable. C. The solution x = –20 should be kept, but x = 5 is unreasonable. D. The solutions x = 5 and x = –20 are unreasonable.

Mathematics

2 answers:

Leona [12.6K] · Answer 1 · 2026-03-30T16:20:51+03:00

By expressing the equation in its standard format, we have: ax^2 + bx + c = 0. First, we expand (x + 15)(x) = 100 to get x^2 + 15x - 100 = 0. Next, from (x + 20)(x - 5) = 0, we find the solutions to be x = -20 and x = 5. Hence, the accurate choice is option B. We discard x = -20 since it is not a valid solution.

PIT_PIT [12.4K] · Answer 2 · 2026-03-30T16:21:27+03:00

Starting with the equation (x + 15)x = 100, we can reformulate it as x^2 + 15x - 100 = 0. This can further be expressed as x^2 + 20x - 5x - 100 = 0, which simplifies to x(x + 20) - 5(x + 20) = 0, resulting in (x - 5)(x + 20) = 0. Thus, we obtain x = 5 or x = -20, but only x = 5 is acceptable since -20 is not valid.