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Determine what c-value will create a perfect square trinomial for the following expression: \( x^{2}+14 x+c \)

Ask by Pritchard Hampton. in the United States
Feb 27,2025

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Tutor-Verified Answer

Answer

c = 49

Solution

To form a perfect square trinomial from x² + 14x + c, c must be equal to the square of half the coefficient of x. Half of 14 is 7, and 7² is 49. Therefore, the trinomial becomes: x² + 14x + 49 = (x + 7)² So, c = 49 creates a perfect square trinomial.

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To create a perfect square trinomial from the expression \( x^{2}+14x+c \), you need to find the right value for \( c \) that makes it a square of a binomial. The formula to do this is \( c = (b/2)^2 \), where \( b \) is the coefficient of \( x \), which in this case is 14. So, \( c = (14/2)^2 = 7^2 = 49 \). Thus, the value of \( c \) that will create a perfect square trinomial is 49. This means the expression will transform into \( (x+7)^2 \), a perfect square trinomial. Perfect square trinomials are not only useful for simplifying expressions, but they also make solving quadratics much easier!

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