Solving Quadratic Equations with Square Roots

Betsy introduces solving equations using square roots, providing a detailed walkthrough of two examples. The first example involves isolating the variable and finding exact solutions, while the second example demonstrates a scenario with no real solution due to a negative square. The video emphasizes the importance of exact answers and understanding the process of isolating variables.

What is the first step in solving equations using square roots as discussed in the video?

• Isolate the variable

• Divide by the coefficient

• Add or subtract terms

• Take the square root

What operation is used to move a subtracted term to the other side of an equation?

• Addition

• Multiplication

• Division

• Subtraction

What is the result of adding 12 to both sides of the equation 3x^2 - 12 = 3?

• 3x^2 = 15

• 3x^2 = 9

• x^2 = 15

• x^2 = 9

When a variable is multiplied by a coefficient, what operation isolates the variable?

• Multiplication

• Division

• Subtraction

• Addition

After dividing by the coefficient 3, what does x^2 equal to?

• 45

• 15

• 5

• 3

What must be considered when taking the square root of both sides of an equation?

• Neither roots

• Both positive and negative roots

• Only negative root

• Only positive root

What is the square root of 25 in the context of solving equations?

• None

• -5

• +5

• +/-5

What is the correct step after isolating x^2 in the equation?

• Take the square root

• Multiply by the coefficient

• Subtract coefficients

• Add coefficients

Why can't a negative number have a real square root?

• It results in a positive number

• It results in zero

• It results in an imaginary number

• It results in a negative number

What does the equation x^2 = -25 imply about the solutions?

• One real solution

• Infinite solutions

• Two real solutions

• No real solutions