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EXAMPLE.

42% 35*

x2 X-3 İXX-22

35** --- 70x 142x

*-3 2X*~3 3142xx - 526x= 354% – 70 14142*

126 = 35* O 4+126 542* = 35% + 56 5 -35%

16 6 + 7 771* = 8

܀ ܀ 3

7* = 56

I 5**

8 - 12
16
215**

128 = 192 2 + 128 315** = 320

I X16

3 = 5 14 ** = 64 4 VU 2

151* =V64 = 8

Of Quadratic Equations, and their

Solutions.

Here are three Fornis of Quadratic Equations,

as follows:

TH

lal

*x + 8x = 240. This is the first Form.. ** 8* = 48.

* = 48. The second Form. N. B. 8 is the Coefficient.

In either of these Forms, this is the practical Rule Take half the known Coefficient and square it; and add thit Square to both Sides of the Equation, and then the Forms will stand thus :

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Now Evolve those Steps, to find the Value of x.

3 vu 2 4 VU 2

5 * +4= V 256 = 16
16 *— 4 = 64=8
17

12
8

12

5 4 6 + 4

And in this Manner you must proceed in all Questions belonging to either of thole Forms.

11 | 16x - ** = 48.

-- XX = 48. This is the third Form.

The Rule for this Form is this. Change all the Signs in the first Step on both sides the Equation, (that is, what' his the Sign + before it, must have the Sign — and what – must have more) and then the Equation will stand thus, putting the Square of x to the left Hand.

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N. B. 64 added to -48, gives the Sum 16.

3 V 2 4 + 8

141 x

8 =V 16 = 4. 151 12

Algebraical

Algebraical Problems, and Questions.

No. 1.

WHAT

HAT Numbers are those whose Difference is

9, and their Sum is 63 ?

*+9= the greater Number.

the least.

1 + 2 32x +9= 63
3-941 2x = 54
4 - 2 5 * = 27 the least Number.
bythe.ft.[6*+9 = 36 the greater Number.

Proof. 36 + 27 = =63

36-27= 9

No. 2. What two Numbers are those whose Difference is 8, and the Quotient of the greater divided by the lefs is 3?

11

*+8= the greater,

* = the less.
3
* +8

- 3 3 X *

41 * + 8 = 3* 4

5 5

2x = 8

6 * = 4 the least Number. bytheift.171 * +8 = 12 the greater.

Proof. 12 - 4 = 8

12 43

5 - 2

No. 3.

No. 3

What Number is that whose third Part exceeds its fourth Párt by 9?

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2 X 3

+ 27

3 4 13

3*

4 3 X4

41 4x = 3x + 108
3* 151 * = 108 the Number.'

4 - 3*

Proof. 108 • 3 = 36

1084 27 And 36

27 9

No. 4.

2

What Number is that whose third Part added to its fourth Part, the Number will be 35 ?

11 x is the Number. Then

47 35 13 3*

105 3 X 4 41 4x + 3x = 420

:: 5. 7* = 420 5 7

161 * = 60 The Number:

3

2 X 3

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4.

Proof. 60 - 320

60 =4 = 15 And 20 +05 35

No. No. 5.

4, is

2 *

%

What Number is that whose third Part equal to its fourth Part + 3?

1 x is the Number. Then

4

+ 3 3

4 2 X 3 3!

3* 12

+9

4 3 X4 14 4* 48 = 3x + 36 4 + 48 15 4* = 3x + 84

84

5 - 3* 16/*

Proof. 84 · 3= 28

84 4 = 21 And 28 - 4 =24 And 21 + 3 = 24

No. 6. What two Numbers are those whose Difference is

and the Difference of their Squares is 95 ? 52

11 x + 5 is the greatest Number:

* is the less Number. 3) *x+10x+25 the Square of the greater, ,

xx the Square of the less. 3 4 5 10x + 25 = 95 5 25

6 10x = 70 6 10 by the 1st. 81 * +5= 12 the greater.

I 2

2

2

14

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71 * = 7 the less

Proof.

I 2 7 5
And 12 X 12 = 144

And 7 x 7 = 49
Then 144 - 49 = 95

No.

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