Algebra 1: Solving Quadratics by Completing the Square

This lesson by Kirk Weiler from eMath Instruction covers solving quadratic equations by completing the square. It begins with a review of solving quadratics using inverses and explains why some equations can't be solved this way. The lesson then reviews polynomial algebra, focusing on perfect square trinomials, and introduces the completing the square method. Through step-by-step practice problems, students learn to transform quadratic equations into a form solvable by inverses. The lesson concludes with a summary of key concepts.

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

• Add a constant to both sides

• Take the square root of both sides

• Square both sides

• Isolate the variable

Why can't we use inverses to solve the equation x^2 + 4x - 21 = 0?

• Because the equation has a negative constant

• Because the equation has no real solutions

• Because x appears more than once

• Because the equation is not in standard form

What is the relationship between the coefficients b and c in a perfect square trinomial?

• c is b divided by 2 and then squared

• c is the square of b

• c is half of b

• c is twice b

In the trinomial x^2 + 20x + 100, what is the value of c?

• 100

• 200

• 20

• 10

What is the first step in the algorithm for completing the square?

• Subtract the constant term from both sides

• Find half the value of the linear coefficient

• Add the linear coefficient to both sides

• Square the linear coefficient

In the equation x^2 + 6x - 16 = 0, what value should be added to both sides to complete the square?

• 6

• 9

• 16

• 25

After completing the square, what form does the equation x^2 + 6x + 9 = 25 take?

• (x + 3)^2 = 25

• (x + 6)^2 = 25

• (x + 5)^2 = 25

• (x + 9)^2 = 25

What is the next step after factoring the trinomial in the completing the square method?

• Multiply both sides by the linear coefficient

• Subtract the linear coefficient from both sides

• Add the constant term to both sides

• Take the square root of both sides

In the equation x^2 - 10x + 25 = 16, what are the solutions for x?

• x = 5 and x = -5

• x = 2 and x = -2

• x = 9 and x = 1

• x = 4 and x = -4

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

• Use inverse operations to solve for the variable

• Square the linear coefficient

• Add the constant term to both sides

• Factor the trinomial