Solving Quadratic Equations by Completing the Square

This video tutorial explains how to solve quadratic equations that cannot be factored normally by using the method of completing the square. It begins with an introduction to the problem and reviews the concept of perfect square trinomials. The tutorial then provides a detailed, step-by-step guide on how to manipulate a quadratic equation to complete the square, emphasizing the importance of balancing the equation. Common mistakes are highlighted, and the correct method is reinforced to ensure understanding.

Why can't the equation x^2 + 16x - 22 be solved by simple factoring?

• The equation is already in its simplest form.

• The equation has no real solutions.

• There are no two numbers that multiply to -22 and add to 16.

• The equation is not a quadratic equation.

What is the first step in completing the square for the equation x^2 + 16x - 22 = 0?

• Subtract 22 from both sides.

• Add 22 to both sides.

• Multiply both sides by 2.

• Divide both sides by 16.

After forming a perfect square trinomial, what is the next step to solve for x?

• Add 8 to both sides.

• Take the square root of both sides.

• Subtract 64 from both sides.

• Multiply both sides by 8.

What is a common mistake when completing the square?

• Adding a different constant to each side.

• Multiplying the equation by zero.

• Dividing the equation by the coefficient of x.

• Forgetting to add the same constant to both sides.

What is the correct solution for x in the equation x^2 + 16x - 22 = 0 after completing the square?

• x = ±√22 - 8

• x = ±√22 + 8

• x = ±√86 + 8

• x = ±√86 - 8