Question

Helpppp!

Fill in the blank with a number to make the expression a perfect square.
x^2+12x+______

Answer 1

x² + 12x + 36

Explanation:

Given the quadratic expression, x² + 12x + ___, with a missing constant value, c:

We can find the value of the constant by taking the coefficient of the middle term, dividing it by 2, and squaring its quotient. In other words,
`((b)/(2))^(2)`. In the given quadratic expression, b = 12. Substitute the value of b = 12 into
`((b)/(2))^(2)`, to find the value of the constant.

x² + 12x +
`((b)/(2))^(2)`

x² + 12x +
`((12)/(2))^(2)`

x² + 12x + (6)²

x² + 12x + 36 ⇒ This is the perfect square trinomial.

Therefore, the missing value for the constant, c, is 36, making the quadratic equation a perfect square trinomial, x² + 12x + 36.