Solving Quadratic Equations by Completing the Square

The video tutorial explains how to solve quadratic equations of the form x^2 + bx + c = 0 using the method of completing the square. It covers the steps to move constant terms, add numbers to complete the square, and factor the equation. The tutorial also addresses how to handle equations with imaginary solutions by simplifying square roots of negative numbers using the imaginary unit 'i'. Finally, it demonstrates solving equations with imaginary solutions through a detailed example.

What is the first step in solving a quadratic equation by completing the square?

• Add a number to both sides to complete the square.

• Take the square root of both sides.

• Move the constant term to the other side.

• Factor the equation into linear factors.

When completing the square, what number should be added to both sides if the middle term is 8x?

• 4

• 8

• 16

• 64

What must you remember to include when taking the square root of both sides of an equation?

• The plus sign

• The minus sign

• The multiplication sign

• The plus or minus sign

How do you express the square root of a negative number in terms of i?

• Divide by 2

• Add the number to itself

• Use the imaginary unit i

• Multiply by -1

What is the simplified form of the square root of negative 12?

• 6i root 2

• 4i root 3

• 3i root 2

• 2i root 3