Question

A quadratic equation is shown: x2 + 18x + 76 = 0 Which of the following is the first correct step to write the above equation in the form (x − p)2 = q, where p and q are integers?

a x2 + 18x + 76 + 9 = 0 + 9
b x2 + 18x + 76 + 5 = 0 + 5
c x2 + 18x + 76 − 5 = 0 − 5
d x2 + 18x + 76 − 9 = 0 − 9

Answer 1

• B) x² + 18x + 76 + 5 = 0 + 5

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Given a quadratic equation:

• x² + 18x + 76 = 0

We need to complete the square.

In order to do so we need to know all terms of the binomial (x - p)².

Its expanded form is:

• (x - p)² = x² - 2px + p²

Comparing with the given equation we see that the first term is x and the value of p can be found as:

• - 2p = 18
• p = - 9

Therefore:

• p² = (-9)² = 81

In order to complete the square we need to add 5 to 76:

• x² + 18x + 76 + 5 = 0 + 5
• (x + 9)² = 5

This gives us q = 5.

The matching answer choice is B.