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Solving quadratics using different methods

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Study note

Rash Abdul

United States of America

DEFAULT (US)

Algebra 1

Solving Equations Using Completing the Square Method

Overview

QUADRATIC EQUATIONS
▪ Methods of Factorization
Factorization Method.
Completing the square Method.
Formula Method.
r
2
FACTORIZATION
usually in the form (x + y) (x - y)
Example: Factorize x² + 8 + 16 = 0
x² x 8 = 8x² →x²+4x+4x+16=0
(x²+4x) (4x+16) =x(x+4) +4(x+4) =0
|X+4=0 or X+4=0
x=-4 (twice) COMPLETING THE SQUARE METHOD
Example: Solve the equation 2x² – 3x − 5 = 0
Divide through by 2: x²
5
=x²-32= 2/20
9
= x² − 3x + 2/8
2
16
—=
-
= [x
= [x - ³] ²
= X
ܚ
I
1/2 coefficient of x =
3
3
9
(²⁄2)² coefficient of x = −³ × – ³ =
=
16
=
=
314 = +√
49
16
[49
5
==
NIC
16
40+9
16
2
+
3x 5
2
SIN
-
9
16
3
-21×²1/2=-2²
X
=
0
3
< -² = ±²
4
= X
= x = ³² ±² 4
+
4
3
7
= x = = ² + ² or ²2 - ²
ΟΥ̓
4
4
10
= x= ¹00 or
4
NIG
= x==
or
-
-4
4
1 Formula Method
Example: Solve the equation 2x² + 6x − 8 = 0
= ax² + bx+c = 0 ·a=2, b=6, and c= -8
=
-b+√b²-4ac
• uses the formula x =
2a
uses the notation ax² + bx + c = 0
Substitute in the equation: x =
=
-6+√6²-4×2×-8
2×2
−6+10
4
-6-10
4
Therefore, x = 1 or – 4
or
-b+√b²-4a
2a
-6+√36+64
4
=
-6+√100
4
=
= or -16 =1 or – 4
4
-6+10
4

Solving Equations Using Completing the Square Method

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Solving Equations Using Completing the Square Method

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.

4.9+

13 M

#1

950 K+

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

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

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

Love this App ❤️, I use it basically all the time whenever I'm studying