What number should be added to the expression [tex]x^2 + 14x[/tex] to change it into a perfect square trinomial?

A. 7
B. 14
C. 28
D. 49

( x + a ) 2 = x 2 + 2 ⋅ x ⋅ a + a 2 ⇒ 2 ⋅ x ⋅ a = 14 x ⇔ 2 a = 14 / : 2 a = 7 ⇒ a 2 = 7 2 = 49 ⇒ a p er f ec t s q u a re t r in o mia l = ( x + 7 ) 2

Answered by kate200468 | 2024-06-24

to be added to x² +14x to change it to a perfect square trinomial is
(14/2)² = 7² = 49 the trinomial is x² + 14x + 49 = (x +7)²

Answered by Poknoy | 2024-06-24

To change the expression x 2 + 14 x into a perfect square trinomial, you need to add 49 . This is found by solving for a in the equation for a perfect square trinomial, leading to a = 7 and thus a 2 = 49 . The correct answer is option D.
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Answered by kate200468 | 2024-10-02