Solve √8x+8 =x+1 State the quadratic equation that occurs after applying the principle of powers to remove the radical. Write the resulting equation in standard form, where a = 1. =0 (Type an expression using x as the variable.)
Solve √8x+8 =x+1 State the quadratic equation that occurs after applying the principle of powers to remove the radical. Write the resulting equation in standard form, where a = 1. =0 (Type an expression using x as the variable.)
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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![**Quadratic Equation Problem Overview**
**Problem:**
Solve the equation involving a radical:
\[ \sqrt{8x + 8} = x + 1 \]
**Task:**
State the quadratic equation that results from applying the principle of powers to remove the radical. Write the resulting equation in standard form, where \(a = 1\).
**Solution Steps:**
1. Square both sides of the equation to eliminate the square root:
\[ (\sqrt{8x + 8})^2 = (x + 1)^2 \]
2. Simplify both sides:
- Left side: \( 8x + 8 \)
- Right side: \( (x + 1)^2 = x^2 + 2x + 1 \)
3. Set the equation to equal zero:
\[ 8x + 8 = x^2 + 2x + 1 \]
\[ 0 = x^2 - 6x - 7 \]
**Result:**
The quadratic equation is \( x^2 - 6x - 7 = 0 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5fc2a9a5-d400-400e-9ea4-34fd53d62fa7%2Fb27dec50-ebd8-4695-bb61-c2d50821096a%2Fodb4obr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Quadratic Equation Problem Overview**
**Problem:**
Solve the equation involving a radical:
\[ \sqrt{8x + 8} = x + 1 \]
**Task:**
State the quadratic equation that results from applying the principle of powers to remove the radical. Write the resulting equation in standard form, where \(a = 1\).
**Solution Steps:**
1. Square both sides of the equation to eliminate the square root:
\[ (\sqrt{8x + 8})^2 = (x + 1)^2 \]
2. Simplify both sides:
- Left side: \( 8x + 8 \)
- Right side: \( (x + 1)^2 = x^2 + 2x + 1 \)
3. Set the equation to equal zero:
\[ 8x + 8 = x^2 + 2x + 1 \]
\[ 0 = x^2 - 6x - 7 \]
**Result:**
The quadratic equation is \( x^2 - 6x - 7 = 0 \).
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