Domanda del libro di testo
Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. See Example 4. -2(x + 3) = -6(x + 7)
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Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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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.6.51
Solve each quadratic equation using the zero-factor property. See Example 5. 25x² + 30x + 9 = 0
Guida verificata passo dopo passo1
Start with the quadratic equation: \(25x^{2} + 30x + 9 = 0\).
Check if the quadratic can be factored into the form \((ax + b)(cx + d) = 0\) by looking for two numbers that multiply to \(25 \times 9 = 225\) and add to \(30\).
Rewrite the middle term \$30x$ as a sum of two terms using the numbers found in the previous step, then group the terms to factor by grouping.
Factor out the greatest common factor (GCF) from each group to express the quadratic as a product of two binomials.
Apply the zero-factor property: set each binomial equal to zero, $ax + b = 0$ and $cx + d = 0$, then solve each equation for \(x\) to find the solutions.
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Quadratic Equations
A quadratic equation is a polynomial equation of degree two, generally written as ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. Solving these equations involves finding the values of x that satisfy the equation.
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Percorso guidato
5:35
Introduction to Quadratic Equations
Zero-Factor Property
The zero-factor property states that if the product of two factors equals zero, then at least one of the factors must be zero. This property is used to solve quadratic equations by factoring them into two binomials set equal to zero.
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Percorso guidato
6:08Factoring
Factoring Quadratic Expressions
Factoring involves rewriting a quadratic expression as a product of two binomials. This step is essential before applying the zero-factor property, as it breaks down the quadratic into simpler expressions that can be individually set to zero.
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Percorso guidato
6:08Factoring
Pratica correlata
Domanda del libro di testo
Determine whether each equation is an identity, a conditional equation, or a contradiction. Give the solution set. See Example 4. 4(x + 7) = 2(x + 12) + 2(x + 1)
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Domanda del libro di testo
Solve each quadratic equation using the zero-factor property. See Example 5.
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Solve each quadratic equation using the quadratic formula. See Example 7.
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Solve each quadratic equation using the zero-factor property. See Example 5. 5x² - 3x - 2 = 0
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Domanda del libro di testo
Solve each quadratic equation using the quadratic formula. See Example 7. x² - 4x + 3 = 0
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