Solving Quadratic Equations Concepts

This lesson reviews the square root property for solving quadratic equations. It covers various examples, including simple cases like x^2 = 9 and more complex ones involving imaginary numbers. The lesson also introduces the concept of completing the square, setting the stage for future lessons.

Why is the square root property important in solving quadratic equations?

• It only works for perfect squares.

• It is faster than any other method.

• It provides a way to solve equations that cannot be factored.

• It is the only method to solve quadratic equations.

When solving x^2 = k, why must we consider both positive and negative roots?

• Because the square root property only applies to positive numbers.

• Because squaring a number always results in a positive value.

• Because negative numbers cannot be squared.

• Because both positive and negative numbers squared give the same result.

What is the solution to x^2 = 121 using the square root property?

• x = -11

• x = 11 or x = -11

• x = 0

• x = 11

How can x^2 = 54 be expressed using square roots?

• x = ±3√6

• x = ±√54

• x = ±3√3

• x = ±6√3

What is the first step in solving 2x^2 + 10 = 152?

• Divide both sides by 2.

• Multiply both sides by 2.

• Subtract 10 from both sides.

• Add 10 to both sides.

What is the solution to 5x^2 + 9 = -7 using imaginary numbers?

• x = ±i√5/5

• x = ±4√5/5

• x = ±4i√5/5

• x = ±4i/5

How do you solve (x - 7)^2 = 64 using the square root property?

• x = 7 ± 64

• x = 7 ± 4

• x = 7 ± 8

• x = 7 ± √64

What is the compact form of the solution for (2x - 1)^2 = 18?

• x = ±3√2 + 1/2

• x = ±3√2/2 + 1

• x = ±3√2 + 1

• x = ±3√2/2

How can you solve 16x^2 - 56x + 49 = -27 by recognizing a perfect square trinomial?

• Factor it into (2x - 7)^2

• Factor it into (4x + 7)^2

• Factor it into (2x + 7)^2

• Factor it into (4x - 7)^2