Domanda del libro di testo
Solve each quadratic equation using the zero-factor property. See Example 5. -4x² + x = -3
64
views
Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 1, Problema R.6.55
Solve each quadratic equation using the square root property. See Example 6. x² - 27 = 0
Guida verificata passo dopo passo1
Start with the given quadratic equation: \(x^{2} - 27 = 0\).
Isolate the squared term by adding 27 to both sides: \(x^{2} = 27\).
Apply the square root property, which states that if \(x^{2} = a\), then \(x = \pm \sqrt{a}\).
Take the square root of both sides: \(x = \pm \sqrt{27}\).
Simplify the square root if possible by factoring out perfect squares: \(\sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}\), so \(x = \pm 3\sqrt{3}\).
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:
3mConcetti 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 = constant by isolating x² and then taking the square root of both sides, considering both positive and negative roots.
Video consigliato:
Percorso guidato
2:20
Imaginary Roots with the Square Root Property
Isolating the Variable Term
Before applying the square root property, the quadratic equation must be rearranged so that the x² term is isolated on one side of the equation. This often involves adding or subtracting constants to both sides to simplify the equation into the form x² = number.
Video consigliato:
Percorso guidato
5:28Equations with Two Variables
Handling Negative Values Under the Square Root
If the constant on the right side of the equation is negative, the solution involves imaginary numbers because the square root of a negative number is not real. In such cases, the solutions are expressed using the imaginary unit i, where i² = -1.
Video consigliato:
Percorso guidato
2:20Imaginary Roots with the Square Root Property
Pratica correlata
Domanda del libro di testo
Solve each quadratic equation using the quadratic formula. See Example 7. -2x² + 4x + 3 = 0
72
views
Domanda del libro di testo
Solve each inequality. Give the solution set using interval notation. See Examples 8 and 9. -3(x - 6) > 2x - 2
49
views
Domanda del libro di testo
Solve each quadratic equation using the quadratic formula. See Example 7. x² - 6x = -7
56
views
Domanda del libro di testo
Solve each quadratic equation using the zero-factor property. See Example 5. x² - 100 = 0
64
views
Domanda del libro di testo
Solve each inequality. Give the solution set using interval notation. See Example 10. -9 ≤ x + 5 ≤ 15
69
views