Subjects

Algebra 1

Overview

Fun Ways to Solve Quadratic Equations!

Name: Knowunity
Brand: Knowunity

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Rash Abdul

@jakey_ndfn

69 Followers

A comprehensive guide to quadratic equations factorization methods, covering three essential solving techniques with detailed examples and step-by-step solutions.

The factorization method breaks down quadratic expressions into simpler factors
Solving quadratic equations by completing the square involves manipulating terms to create a perfect square trinomial
The quadratic formula method example demonstrates solving equations using the universal formula -b±√(b²-4ac)/2a
Each method offers unique advantages for different types of quadratic equations
Understanding all three methods enables students to choose the most efficient approach for any given problem

11/4/2023

185

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Completing the Square Method

This section details the process of completing the square, a sophisticated method for solving quadratic equations by creating perfect square trinomials.

Example: The equation 2x² - 3x - 5 = 0 is solved step by step, beginning with dividing all terms by 2

Vocabulary: A perfect square trinomial is an expression that can be written as (x + p)²

Highlight: The method involves adding and subtracting specific terms to create a perfect square, leading to solutions x = 5/4 or -1

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Formula Method

The quadratic formula provides a universal solution method for any quadratic equation in standard form.

Definition: The quadratic formula x = (-b±√(b²-4ac))/2a solves any equation in the form ax² + bx + c = 0

Example: For 2x² + 6x - 8 = 0, where a=2, b=6, and c=-8, the solution process demonstrates the formula's application

Highlight: The method yields solutions x = 1 or -4, showing how the formula can efficiently solve equations that might be challenging with other methods

View

Factorization Method

This section introduces the fundamental approach to solving quadratic equations through factorization. The method typically involves rearranging terms into the form (x + y)(x - y).

Example: x² + 8 + 16 = 0 is solved through factorization by rearranging terms into x(x+4) + 4(x+4) = 0

Definition: Factorization is the process of breaking down a quadratic expression into the product of its factors.

Highlight: The solution x = -4 appears twice in this example, indicating a repeated root.

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Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

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Knowunity is the # 1 ranked education app in five European countries

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I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

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The application is very simple and well designed. So far I have found what I was looking for :D

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Subjects

Algebra 1

Overview

Fun Ways to Solve Quadratic Equations!

Rash Abdul

@jakey_ndfn

69 Followers

A comprehensive guide to quadratic equations factorization methods, covering three essential solving techniques with detailed examples and step-by-step solutions.

The factorization method breaks down quadratic expressions into simpler factors
Solving quadratic equations by completing the square involves manipulating terms to create a perfect square trinomial
The quadratic formula method example demonstrates solving equations using the universal formula -b±√(b²-4ac)/2a
Each method offers unique advantages for different types of quadratic equations
Understanding all three methods enables students to choose the most efficient approach for any given problem

11/4/2023

185

9th/10th

Algebra 1

Completing the Square Method

This section details the process of completing the square, a sophisticated method for solving quadratic equations by creating perfect square trinomials.

Example: The equation 2x² - 3x - 5 = 0 is solved step by step, beginning with dividing all terms by 2

Vocabulary: A perfect square trinomial is an expression that can be written as (x + p)²

Highlight: The method involves adding and subtracting specific terms to create a perfect square, leading to solutions x = 5/4 or -1

Formula Method

The quadratic formula provides a universal solution method for any quadratic equation in standard form.

Definition: The quadratic formula x = (-b±√(b²-4ac))/2a solves any equation in the form ax² + bx + c = 0

Example: For 2x² + 6x - 8 = 0, where a=2, b=6, and c=-8, the solution process demonstrates the formula's application

Highlight: The method yields solutions x = 1 or -4, showing how the formula can efficiently solve equations that might be challenging with other methods

Factorization Method

This section introduces the fundamental approach to solving quadratic equations through factorization. The method typically involves rearranging terms into the form (x + y)(x - y).

Example: x² + 8 + 16 = 0 is solved through factorization by rearranging terms into x(x+4) + 4(x+4) = 0

Definition: Factorization is the process of breaking down a quadratic expression into the product of its factors.

Highlight: The solution x = -4 appears twice in this example, indicating a repeated root.

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Download in

Google Play

Download in

App Store

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User