Solving Quadratic Equations with Inverse Operations

The video tutorial covers solving quadratic equations using inverse operations. It includes three examples, starting with a basic equation and progressing to more complex ones. The instructor explains each step, emphasizing the use of inverse operations to isolate the variable. The tutorial also discusses the nature of solutions, including irrational and rational numbers, and provides strategies for approximating square roots.

What is the first step in solving a quadratic equation using inverse operations?

• Divide both sides by a constant

• Subtract a constant from both sides

• Add a constant to both sides

• Multiply both sides by a constant

In the first example, what operation is used to move the positive 19 to the other side of the equation?

• Addition

• Multiplication

• Division

• Subtraction

After isolating x² in the first example, what is the next step to solve for x?

• Subtract 6 from both sides

• Add 6 to both sides

• Take the square root of both sides

• Multiply both sides by -1

What are the solutions for x in the first example?

• x = ±√4

• x = ±√3

• x = ±√6

• x = ±√9

In the second example, what is the first operation performed to isolate the term with x?

• Add 45 to both sides

• Multiply both sides by 3

• Subtract 45 from both sides

• Divide both sides by 3

What is the result of dividing 87 by 3 in the second example?

• 27

• 29

• 31

• 30

What are the solutions for x in the second example?

• x = 6 ± √9

• x = 6 ± √29

• x = 6 ± √21

• x = 6 ± √19

In the third example, what is the result of dividing 64 by 4?

• 17

• 16

• 15

• 14

What are the solutions for x in the third example?

• x = 2 or x = -2

• x = 4 or x = -4

• x = 8 or x = -8

• x = 0 or x = -8

What is the main goal when solving quadratic equations using inverse operations?

• To eliminate the square root

• To balance both sides of the equation

• To isolate the variable x

• To isolate the constant term