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Ex. 2. What are the values of x in the equation

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These values of x may be verified as in the pre beding example.

Ex. 3. What are the values of x in the equation x2+6x=-8?

Ans. x=-2 or -4. Ex. 4. What are the values of x in the equation x2+6x=27?

Ans. x=+3 or -9. Ex. 5. What are the values of x in the equation 2x2+8x-20=70?

Ans. x=+5 or -9.

Ex. 6. What are the values of x in the equation

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Ex. 7. What are the values of x in the equation

x2+14x-2

x2-10x+50=

?

5

Ans. x=+9 or +7.

Ex. 8. What are the values of x in the equation

3x2-6x-74=31?

Ans. x=+7 or -5.

Ex. 9. What are the values of x in the equation

10

x2+2x

x2+2x

90

?

7

7

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Ex. 10. What are the values of x in the equation

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(169.) The preceding method of solving a complete equation is applicable to all cases; nevertheless, it sometimes leads to inconvenient fractions. For, in order to reduce a given equation to the required form, x2+2px=q, we must divide by the coefficient of x2, which it is often impossible to do without a remainder. Let, then, the equation be represented by the form ax2+bx=c.

Multiply each member of the equation by 4a, and

it becomes

4a2x2+4abx=4ac.

Adding b2 to both members, we have

4a2x2+4abx+b2=4ac+b2.

The first member of the equation is now a complete square, and its square root is 2ax+b.

(170.) Hence, for completing the square, we may use the following

RULE.

Multiply the equation by four times the coefficient of x', and add to both sides the square of the coeffi cient of x.

If the coefficient of x is unity, this rule becomes, Multiply the equation by four, and add to each member the square of the coefficient of x.

Either of these methods of completing the square QUEST.-What inconvenience sometimes results from the preceding method of solution? What method is free from this inconvenience?

may be practiced at pleasure; but the first method is to be preferred, except when its application would involve inconvenient fractions.

Ex. 11. What are the values of x in the equation

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Ex. 12 What are the values of x in the equation

Transimig,

3x2+2x-9-76?

3x2+2x=85

Multiplying each member 12, we have

36x2+24x=1020.

Adding the square of 2 to each member, we obtain 36x2+24x+4=1024.

Extracting the square root,

6x+2=±32.

Whence 6x=-2+32=+30 or -34;

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Ex. 13. What are the values of x in the equation

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QUEST.-When is the first method to be preferred?

3x2-2x=133.

Completing the square and extracting the root, 6x=2+40=42 or -38.

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Ex. 14. What are the values of x in the equation

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Clearing of fractions, completing the square, and extracting the root, we have

Whence

24x=8±28=36 or -20.

x=1 or -.

Ex. 15. What are the values of x in the equation

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Ex. 16. What are the values of x in the equation

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Ex. 17. What are the values of x in the equation

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Ex. 18. What are the values of x in the equation

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Ex. 19. What are the values of x in the equation

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Ex. 20. What are the values of x in the equation

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Ex. 21. What are the values of x in the equation

x2+8x+50=35?

Ans. x=-3 or -5.

Ex. 22. What are the values of x in the equation 7x+35=11-3x-x2?

Ans. x=-4 or -6.

Ex. 23. What are the values of x in the equation

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Ex. 24. What are the values of x in the equation

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Ex. 25. What are the values of x in the equation

2x2

+4x+18=6-2x ?

3

Ans. x=-3 or -6.

Ex. 26. What are the values of x in the equation

2x2+9x+25=23+4x ?

1

Ans. x= -2 or

2'

Ex. 27. What are the values of x in the equation

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