Question

stephanie started to complete the square, but only found one of the solutions. what is the other solution?
$x^2 + 4x = 77$
$x^2 + 4x + 4 = 77 + 4$
$(x + 2)^2 = 81$
$x + 2 = 9$
$x = 7$

Explanation:

Step1: Recall square root property

When we have \((x + 2)^2 = 81\), by the square root property, \(x + 2=\pm\sqrt{81}\).

Step2: Consider the negative root

We know \(\sqrt{81} = 9\), so we also need to consider \(x + 2=- 9\) (since we only considered \(x + 2 = 9\) before).

Step3: Solve for x

Subtract 2 from both sides: \(x=-9 - 2=-11\).

Answer:

\(x = - 11\)