8.10.5 Solving Quadratic Equations by Any Method

Algebra 18.10.5 Solving Quadratic Equations by Any Method

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Now, combine your new understanding of factoring with using the zero product property to solve equations.

Solve the equation $2 x^{2} - 7 x + 5 = 0$ by any method. Be prepared to explain your reasoning.

Enter the solution to the equation $2 x^{2} - 7 x + 5 = 0$ and your explanation.

Compare your answer:

$x = \frac{5}{2}$ (or 2.5) and $x = 1$ . Rewriting the expression in factored form gives $(2 x - 5) (x - 1) = 0$ . Using the zero product property: $2 x - 5 = 0$ or $x - 1 = 0$ , so $x = \frac{5}{2}$ and $x = 1$ .

Building Character: Curiosity

An illustrated person kneels outdoors, holding a magnifying glass and examining orange flowers, with a question mark in a speech bubble above their head. Pine trees and clouds are in the background.

People typically spend more time learning about things they are curious about and more readily remember the information. Curious people tend to be happier individuals.

Think about your current sense of curiosity. Are the following statements true for you?

When I didn’t know the answer to a question, I couldn’t rest until I figured it out.
I explored a completely new idea or topic—just for the fun of it.

Don’t worry if none of these statements are true for you. Developing this trait takes time. Your first step starts today!

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- Publication date: Jun 4, 2025
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