Question

Solve using the quadratic formula. $$ 3(t-3)-t(t-5)=7 t $$

   Solve using the quadratic formula.
$$
3(t-3)-t(t-5)=7 t
$$

Elementary Algebra

Elementary Algebra

John Redden 1st Edition

Chapter 9, Problem 88

Instant Answer

Solved by Expert Victor Salazar

02/04/2022

Step 1

Distribute the 3 in the first term and the -t in the second term to get: $$ 3t - 9 - t^2 + 5t = 7t $$ Show more…

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Solve using the quadratic formula. $$ 3(t-3)-t(t-5)=7 t $$

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Key Concepts

Quadratic Equations

A quadratic equation is a polynomial equation of degree two, typically written in the form ax² + bx + c = 0. Solving quadratic equations involves finding the roots, which are the values that satisfy the equation. Understanding the structure of quadratic equations is essential for selecting the appropriate method, such as factoring, completing the square, or using the quadratic formula.

Quadratic Formula

The quadratic formula is a universal method for solving any quadratic equation when it is expressed in standard form. It is given by x = (-b ± ?(b² - 4ac)) / (2a). This formula leverages the discriminant, b² - 4ac, to determine the nature and number of the roots, making it a powerful tool when other methods, such as factoring, are not straightforward.

Algebraic Manipulation

Algebraic manipulation involves the use of techniques such as distribution, combining like terms, and rearranging equations to transform an expression into a more convenient form. In the context of solving quadratic equations, it is often necessary to expand expressions and collect like terms in order to rewrite the equation in the standard quadratic form before applying the quadratic formula.

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