Question

Solve by completing the square. $$ y 2-2 y-74=0 $$

   Solve by completing the square.
$$
y 2-2 y-74=0
$$

Elementary Algebra

Elementary Algebra

John Redden 1st Edition

Chapter 9, Problem 20

Instant Answer

Solved by Expert Victor Salazar

02/04/2022

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To do this, we need to complete the square for the equation $y^2-2y-74=0$. Show more…

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Solve by completing the square. $$ y 2-2 y-74=0 $$

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Key Concepts

Quadratic Equation

A quadratic equation is a second-degree polynomial equation usually presented in the form ax² + bx + c = 0. It is foundational in algebra and represents curves and parabolic graphs. Solving quadratic equations is a key skill, and there are several methods for doing so, including factoring, applying the quadratic formula, and completing the square.

Completing the Square

Completing the square is a systematic algebraic technique used to transform a quadratic equation into a perfect square trinomial, which makes it easier to solve. The method involves isolating the quadratic and linear terms, then adding and subtracting an appropriate constant to form a perfect square. This transformed equation can be solved using the square root property, providing an alternative to the quadratic formula.

Perfect Square Trinomial

A perfect square trinomial is an algebraic expression that can be written as the square of a binomial, meaning it fits the form (x + d)² = x² + 2dx + d². Recognizing or constructing a perfect square trinomial is essential in the process of completing the square because it simplifies the equation and allows for straightforward application of the square root method.

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