Find all real solutions of the equation (x – 6)² = 25. with x1 < x2 and x2 Enter an integer or decimal number [more..1

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Problem Statement:**

Find all real solutions of the equation \((x - 6)^2 = 25\).

**Solutions:**

\( x_1 = \) [Enter an integer or decimal number]

and

\( x_2 = \) [Enter an integer or decimal number] 

with \( x_1 < x_2 \).

---

**Explanation:**

The equation \((x - 6)^2 = 25\) is a quadratic equation. By taking the square root of both sides, \(x - 6 = \pm 5\), the possible solutions for \(x\) are computed by solving \(x - 6 = 5\) and \(x - 6 = -5\). 

Remember to order the solutions such that \(x_1 < x_2\).
Transcribed Image Text:**Problem Statement:** Find all real solutions of the equation \((x - 6)^2 = 25\). **Solutions:** \( x_1 = \) [Enter an integer or decimal number] and \( x_2 = \) [Enter an integer or decimal number] with \( x_1 < x_2 \). --- **Explanation:** The equation \((x - 6)^2 = 25\) is a quadratic equation. By taking the square root of both sides, \(x - 6 = \pm 5\), the possible solutions for \(x\) are computed by solving \(x - 6 = 5\) and \(x - 6 = -5\). Remember to order the solutions such that \(x_1 < x_2\).
The given quadratic equation is:

\[ 4p^2 + p - 9 = 0 \]

Below the equation, there is a text box labeled:

\[ p = \]

This setup is typically used to solve for the variable \( p \) using algebraic methods such as factoring, completing the square, or applying the quadratic formula.
Transcribed Image Text:The given quadratic equation is: \[ 4p^2 + p - 9 = 0 \] Below the equation, there is a text box labeled: \[ p = \] This setup is typically used to solve for the variable \( p \) using algebraic methods such as factoring, completing the square, or applying the quadratic formula.
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