Textbook Question
Solve each equation in Exercises 1 - 14 by factoring.
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1. Equations & Inequalities
Intro to Quadratic Equations
1:27 minutesProblem 15
Textbook Question
Solve each equation in Exercises 15–34 by the square root property.
Verified step by step guidance1
Start with the given equation: \$3x^2 = 27$.
Isolate the \(x^2\) term by dividing both sides of the equation by 3: \(x^2 = \frac{27}{3}\).
Simplify the right side to get \(x^2 = 9\).
Apply the square root property, which states that if \(x^2 = a\), then \(x = \pm \sqrt{a}\), so here \(x = \pm \sqrt{9}\).
Simplify the square root to express the solutions for \(x\).
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1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Square Root Property
The square root property states that if x² = k, then x = ±√k. This property is used to solve quadratic equations that can be written in the form x² = a constant, allowing you to find the values of x by taking the square root of both sides.
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Isolating the Variable Term
Before applying the square root property, the equation must be manipulated so that the squared term is isolated on one side. This often involves dividing or multiplying both sides of the equation to simplify it to the form x² = number.
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Simplifying Square Roots
After taking the square root of both sides, it is important to simplify the radical expression. This includes factoring out perfect squares and expressing the root in simplest form, which helps in finding exact solutions.
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