What is the value of c such that: x² + 14x + c, is a perfect-square trinomial?

Solution:

A perfect square trinomial is defined as an algebraic expression that is obtained by squaring a binomial expression.

It is of the form ax² + bx + c.

Here a, b, and c are real numbers and a ≠ 0.

The given equation is x² + 14x + c

To find the value of c

We can take half of linear coefficient and square it

14/2 = 7

72 = 49

Therefore, the value of c is 49.

What is the value of c such that: x² + 14x + c, is a perfect-square trinomial?

Summary:

The value of c such that: x² + 14x + c, is a perfect-square trinomial is 49.