Solve the equation algebraically 2+ x 9 ||
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Concept explainers
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
![**Solve the equation algebraically**
\[
3^{-x^2 + x} = \frac{1}{9}
\]
This equation requires solving the expression with a base of 3 raised to the power of \(-x^2 + x\). The equation is set equal to the fraction \(\frac{1}{9}\). Note that \(\frac{1}{9}\) can be expressed as \(3^{-2}\). Thus, equate the exponents:
\[
-x^2 + x = -2
\]
Re-arrange to form a quadratic equation:
\[
x^2 - x - 2 = 0
\]
This quadratic equation can be solved using factoring, completing the square, or the quadratic formula.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc66d6164-0234-4873-be88-e969e82164f6%2F6601ab69-930f-49f7-8c44-b1b7bb5ffef4%2Ffttuiup_processed.png&w=3840&q=75)
Transcribed Image Text:**Solve the equation algebraically**
\[
3^{-x^2 + x} = \frac{1}{9}
\]
This equation requires solving the expression with a base of 3 raised to the power of \(-x^2 + x\). The equation is set equal to the fraction \(\frac{1}{9}\). Note that \(\frac{1}{9}\) can be expressed as \(3^{-2}\). Thus, equate the exponents:
\[
-x^2 + x = -2
\]
Re-arrange to form a quadratic equation:
\[
x^2 - x - 2 = 0
\]
This quadratic equation can be solved using factoring, completing the square, or the quadratic formula.
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