Textbook Question
Solve each equation in Exercises 65–74 using the quadratic formula. x2 - 6x + 10 = 0
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1. Equations & Inequalities
The Quadratic Formula
1:12 minutesProblem 87
Textbook Question
Solve each equation in Exercises 83–108 by the method of your choice.
Verified step by step guidance1
Start with the given equation: \$3x^2 = 60$.
Isolate the \(x^2\) term by dividing both sides of the equation by 3: \(x^2 = \frac{60}{3}\).
Simplify the right side to get \(x^2 = 20\).
To solve for \(x\), take the square root of both sides: \(x = \pm \sqrt{20}\).
Simplify the square root if possible to express the solution in simplest radical form.
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1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Solving Quadratic Equations
A quadratic equation is a polynomial equation of degree two, typically in the form ax² + bx + c = 0. Solving such equations involves finding the values of x that satisfy the equation. Methods include factoring, completing the square, using the quadratic formula, or isolating the variable when possible.
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Isolating the Variable
Isolating the variable means manipulating the equation to get the variable alone on one side. This often involves performing inverse operations such as division, multiplication, addition, or subtraction. For example, dividing both sides by the coefficient of x² helps simplify the equation before solving.
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Square Roots and Their Properties
When an equation involves x², taking the square root of both sides can help solve for x. Remember that both positive and negative roots must be considered, since (±√a)² = a. Understanding how to apply square roots correctly is essential for solving quadratic equations without linear terms.
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