Domanda del libro di testo
Solve each equation in Exercises 15–34 by the square root property.
1028
views
Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 2, Problema 16
Solve each equation in Exercises 15–34 by the square root property.
Guida verificata passo dopo passo1
Start with the given equation: \(5x^2 = 45\).
Divide both sides of the equation by 5 to isolate \(x^2\): \(x^2 = \frac{45}{5}\).
Simplify the right side: \(x^2 = 9\).
Apply the square root property, which states that if \(x^2 = a\), then \(x = \pm \sqrt{a}\): \(x = \pm \sqrt{9}\).
Simplify the square root to find the two possible values for \(x\).
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:
1mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Square Root Property
The square root property states that if x² = k, then x = ±√k. This method is used to solve quadratic equations that can be written in the form x² = a constant. It involves isolating the squared term and then taking the square root of both sides, remembering to include both positive and negative roots.
Video consigliato:
02:20
Imaginary Roots with the Square Root Property
Isolating the Variable Term
Before applying the square root property, the equation must be manipulated so that the squared term stands alone on one side. This often involves dividing or multiplying both sides of the equation to simplify it. For example, dividing both sides of 5x² = 45 by 5 isolates x².
Video consigliato:
05:28Equations with Two Variables
Simplifying Square Roots
After taking the square root of both sides, simplifying the radical expression is necessary. This includes factoring out perfect squares from under the root to write the answer in simplest form. For instance, √9 simplifies to 3, which makes the solution clearer and more exact.
Video consigliato:
02:20Imaginary Roots with the Square Root Property
Pratica correlata
Domanda del libro di testo
Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(6x + 1) = x - 1
469
views
Domanda del libro di testo
In Exercises 1–26, solve and check each linear equation. 4(x + 9) = x
900
views
Domanda del libro di testo
Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3
y = x + 2
876
views
Domanda del libro di testo
Find each product and write the result in standard form. (3 + 5i)(3 - 5i)
835
views
Domanda del libro di testo
Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3
y = x - 2
1144
views