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:**
Solve the equation for \( c \):
The product of \((c - 1)\) and \((c - 10)\) is equal to 190. Find \( c \).
\[ c = \underline{\hspace{3cm}} \]
**Solution Explanation:**
To solve for \( c \), we need to expand the product and set it equal to 190:
1. Expand the expression:
\((c - 1)(c - 10) = c^2 - 10c - c + 10 = c^2 - 11c + 10\)
2. Set up the equation:
\(c^2 - 11c + 10 = 190\)
3. Simplify the equation:
\(c^2 - 11c + 10 - 190 = 0\)
\(c^2 - 11c - 180 = 0\)
4. Solve the quadratic equation using factoring, completing the square, or the quadratic formula.
**Note:** The blank box is where the solution for \( c \) should be entered once calculated.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa1e1d114-cba9-4c4f-a9ab-1a346fb28105%2F1a2c19ad-170e-4823-9ca9-91da03cd531f%2F8rfv21_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Solve the equation for \( c \):
The product of \((c - 1)\) and \((c - 10)\) is equal to 190. Find \( c \).
\[ c = \underline{\hspace{3cm}} \]
**Solution Explanation:**
To solve for \( c \), we need to expand the product and set it equal to 190:
1. Expand the expression:
\((c - 1)(c - 10) = c^2 - 10c - c + 10 = c^2 - 11c + 10\)
2. Set up the equation:
\(c^2 - 11c + 10 = 190\)
3. Simplify the equation:
\(c^2 - 11c + 10 - 190 = 0\)
\(c^2 - 11c - 180 = 0\)
4. Solve the quadratic equation using factoring, completing the square, or the quadratic formula.
**Note:** The blank box is where the solution for \( c \) should be entered once calculated.
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