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Lesson 2C. Solving Quadratic Equations by Completing the Square
Activity 1: PST to Square of a Binomial!
Were you able to express each perfect square trinomial as a square of a binomial?
Were you able to express each perfect square trinomial as a square of a binomial?
Let's further strengthen your knowledge and skills in writing perfect square trinomials by doing the next activity.
Activity 2:
Make It Perfect!
Was it easy for you to determine the number that must be added to the terms of a polynomial to make it a perfect square trinomial? Were you able to figure out how it can be easily done? If not, you can watch this video for better understanding of the lesson..
Was it easy for you to determine the number that must be added to the terms of a polynomial to make it a perfect square trinomial? Were you able to figure out how it can be easily done? If not, you can watch this video for better understanding of the lesson..
TIP: Add a square of one half of the coefficient of the middle term.
(b/2)^2
Making Perfect Square Trinomials
Solving Quadratic Equations by completing the square
Solving Quadratic Equations by completing the square
steps in solving quadratic equations by completing the square
steps in solving quadratic equations by completing the square
Divide both sides of the equation by a then simplify.
Write the equation such that the terms with variables are on the left side of the equation and the constant term is on the right side.
Add the square of one half of the coefficient of x on both sides of the resulting equation. The left side of the equation becomes a perfect square trinomial.
Express the perfect square trinomial on the left side of the of the equation as a square of a binomial.
Solve the resulting quadratic equation by extracting the square root.
Solve the resulting linear equations.
Check the solutions obtained agains the original equation.
EXAMPLES
Activity 3:
Let's Practice!
Was it easy for you to find the solutions of the quadratic equations by completing the square?
Now, let's get deeper!
Please Watch This!
Activity 4:
Activity 4:
Designing packaging boxes
Designing packaging boxes
Perform the following activity.
A. designing open boxes
A. designing open boxes
Make sketch plans of 5 rectangular boxes such that:
a. the heights of the boxes are the same; and
b. the boxes can hold 240 cubic cm, 270 cubic cm, 504 cubic cm, 810 cubic cm, and 468 cubic cm, respectively.
Write a quadratic equation that would represent the volume of each box.
Solve each quadratic equation by completing the square to determine the dimensions of the materials to be used in constructing each box.
B. designing covers of the open boxes
B. designing covers of the open boxes
Make sketch plans of covers of the open boxes in Part A such that:
a. the heights of the covers are the same; and
b. the base of each cover is rectangular.
Write a quadratic equation that would represent the volume of the box's cover.
Solve each quadratic equation by completing the square to determine the dimensions of the materials to be used in constructing the box's cover.
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