Wood Phillips
07/26/2023 · High School
ide what number must be added to both sides of the equation to make the left side a perfect square trinomial, then fact \( y^{2}-8 y=5 \) d a number to both sides of the equation to make the left side a perfect square trinomial. \( \begin{array}{l}-8 y+\square=5+\square \\ \text { ype integers or simplified fractions.) }\end{array} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To make the left side of the equation \( y^2 - 8y = 5 \) a perfect square trinomial, we need to complete the square.
1. Start with the equation:
\[
y^2 - 8y = 5
\]
2. To complete the square, take the coefficient of \( y \) (which is \(-8\)), divide it by 2, and then square it:
\[
\left(-\frac{8}{2}\right)^2 = (-4)^2 = 16
\]
3. Add this number (16) to both sides of the equation:
\[
y^2 - 8y + 16 = 5 + 16
\]
4. This simplifies to:
\[
y^2 - 8y + 16 = 21
\]
5. Now, the left side is a perfect square trinomial, which can be factored as:
\[
(y - 4)^2 = 21
\]
So, the number that must be added to both sides of the equation is \( 16 \).
In summary, the completed equation is:
\[
y^2 - 8y + 16 = 5 + 16
\]
or
\[
y^2 - 8y + \square = 5 + \square
\]
where \( \square = 16 \).
Quick Answer
The number to add to both sides is \( 16 \). The completed equation is:
\[
y^2 - 8y + 16 = 5 + 16
\]
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