Question
Determine what c-value will create a perfect square trinomial for the following expression: \( x^{2}-15 x+c \)
Ask by Lambert Summers. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The value of c is 225/4.
Solution
To create a perfect square trinomial, the quadratic expression should match the form (x - a)², which expands to x² - 2ax + a².
Given the quadratic x² - 15x + c, set -2a equal to -15:
-2a = -15 → a = 15/2
Now, find c by realizing that a² is the constant term:
c = a² = (15/2)² = 225/4
Thus, the value of c that creates a perfect square trinomial is 225/4.
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Simplify this solution Bonus Knowledge
To create a perfect square trinomial from the expression \( x^{2}-15x+c \), we can use the following formula. The c-value must be equal to half of the coefficient of x, squared. In this case, half of -15 is -7.5, and squaring it gives us 56.25. So, for this expression to be a perfect square trinomial, \( c \) should equal 56.25. Now, you can rewrite the expression as \( (x - 7.5)^{2} \) when \( c = 56.25 \). Perfectly square it up!
