# How do you find the value of c that makes x^2-15x+c into a perfect square?

Dec 23, 2016

$c = \frac{225}{4}$

#### Explanation:

By the property ${\left(a + c\right)}^{2} = {a}^{2} + 2 a c + {c}^{2}$, we can solve for $c$.

$2 a c = - 15$

$2 \left(1\right) \left(c\right) = - 15$

$c = - \frac{15}{2}$

The value of $c$ needs to be a perfect square, so $c = {\left(- \frac{15}{2}\right)}^{2} = \frac{225}{4}$.

Hopefully this helps!