Ch. 4 - Exponential and Logarithmic Functions

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo

Blitzer 8th Edition

Ch. 4 - Exponential and Logarithmic Functions

Problema 138

Capitolo 5, Problema 138

Exercises 137–139 will help you prepare for the material covered in the next section. Solve: x(x - 7) = 3.

Guida verificata passo dopo passo

Start by expanding the left side of the equation:

x (x - 7) = x \cdot x - x \cdot 7 = x^{2} - 7x

Rewrite the equation with the expanded form:

x^{2} - 7x = 3

Bring all terms to one side to set the equation equal to zero:

x^{2} - 7x - 3 = 0

Identify the coefficients for the quadratic equation in standard form

ax^2 + bx + c = 0

: here,

a = 1

b = -7

, and

c = -3

Use the quadratic formula to solve for

x

x = \(\frac{-b \pm \sqrt{b^2 - 4ac}\)}{2a}

. Substitute the values of

a

b

, and

c

into the formula.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Durata del video:

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Expanding and Simplifying Algebraic Expressions

This involves applying the distributive property to multiply terms within parentheses and then combining like terms. For example, expanding x(x - 7) results in x² - 7x, which simplifies the equation for easier manipulation.

Video consigliato:

05:07

Simplifying Algebraic Expressions

Solving Quadratic Equations

Quadratic equations are polynomial equations of degree two, typically in the form ax² + bx + c = 0. Solving them can involve factoring, completing the square, or using the quadratic formula to find the values of x that satisfy the equation.

Video consigliato:

06:08

Solving Quadratic Equations by Factoring

Setting Equations to Zero

To solve quadratic equations, it is essential to rewrite the equation so that one side equals zero. This allows the use of factoring or the quadratic formula by isolating all terms on one side, creating a standard form ax² + bx + c = 0.

Video consigliato:

03:42

Finding Zeros & Their Multiplicity

Pratica correlata

Domanda del libro di testo

In Exercises 125–128, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.

log_b (xy)⁵ = (log_b x + log_b y)⁵

944

views

Domanda del libro di testo

Exercises 137–139 will help you prepare for the material covered in the next section. Solve for x: a(x - 2) = b(2x + 3)

696

views

Domanda del libro di testo

Without using a calculator, find the exact value of: [log₃ 81 - log_𝝅 1]/[log_2√2 8 - log 0.001]

1483

views

rank