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: \( (y - 4)^2 = 21 \)

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Add \(16\) to both sides to make the left side a perfect square trinomial.
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