Reese Norris
07/26/2024 · Junior High School
Decide what number must be added to both sides of the equation to make the left side a perfect sq \( y^{2}-8 y=5 \) Add a number to both sides of the equation to make the left side a perfect square trinomial. \( y^{2}-8 y+16=5+16 \) (Type integers or simplified fractions.) Factor the left side of the equation and simplify the right side. (Type integers or simplified fractions.) (Typ
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ically, the number added is the square of half the coefficient of the linear term.)
To make the left side of the equation a perfect square trinomial, we need to add the square of half the coefficient of the linear term. In this case, the linear term is \(-8y\), and half of the coefficient is \(-4\). The square of \(-4\) is \(16\).
So, we add \(16\) to both sides of the equation:
\( y^{2} - 8y + 16 = 5 + 16 \)
Now, the left side of the equation is a perfect square trinomial, which can be factored as:
\( (y - 4)^2 = 21 \)
The right side of the equation simplifies to:
\( 5 + 16 = 21 \)
Therefore, the number that must be added to both sides of the equation to make the left side a perfect square trinomial is \(16\), and the factored form of the equation is:
\( (y - 4)^2 = 21 \)
Quick Answer
Add \(16\) to both sides to make the left side a perfect square trinomial.
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