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,...
Related questions
Question
Solve each equation using the square roots method.
![**Quadratic Equations:**
Here are two quadratic equations to solve:
**17.** \(2x^2 - 9 = 55\)
To solve, start by isolating the variable term:
\[ 2x^2 = 55 + 9 \]
\[ 2x^2 = 64 \]
Next, divide by 2:
\[ x^2 = 32 \]
Finally, take the square root of both sides:
\[ x = \pm \sqrt{32} \]
\[ x = \pm 4\sqrt{2} \]
---
**18.** \(9x^2 + 3 = 111\)
First, subtract 3 from both sides to isolate the variable term:
\[ 9x^2 = 111 - 3 \]
\[ 9x^2 = 108 \]
Divide by 9:
\[ x^2 = 12 \]
Take the square root of both sides:
\[ x = \pm \sqrt{12} \]
\[ x = \pm 2\sqrt{3} \]
These solutions provide the values of \(x\) that satisfy the given equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78a256bd-ea52-4682-957b-1448c364f8ac%2F5de85ace-c959-4c0b-a86d-ccd07e3792cb%2F71k8vga_processed.png&w=3840&q=75)
Transcribed Image Text:**Quadratic Equations:**
Here are two quadratic equations to solve:
**17.** \(2x^2 - 9 = 55\)
To solve, start by isolating the variable term:
\[ 2x^2 = 55 + 9 \]
\[ 2x^2 = 64 \]
Next, divide by 2:
\[ x^2 = 32 \]
Finally, take the square root of both sides:
\[ x = \pm \sqrt{32} \]
\[ x = \pm 4\sqrt{2} \]
---
**18.** \(9x^2 + 3 = 111\)
First, subtract 3 from both sides to isolate the variable term:
\[ 9x^2 = 111 - 3 \]
\[ 9x^2 = 108 \]
Divide by 9:
\[ x^2 = 12 \]
Take the square root of both sides:
\[ x = \pm \sqrt{12} \]
\[ x = \pm 2\sqrt{3} \]
These solutions provide the values of \(x\) that satisfy the given equations.
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