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Let the affirmative value be taken, and complete

the square, x2—x+1=30+1=121

4

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10. Given 2x2+√/18x2+9x=54-x, to find the value of x.

By transposition, 2x2+x+√/18x2+9x=54;
.. (Def. 14.) 2x2+x+31√/2x2+x=54;

completing the square, 2x2+x+3、/2x2+x+

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extracting the root, √2x2+x+3=±

√2x2+x=6, or -9;

squaring each side, 2x2+x=36, or 81;

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81

15

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Let the first value be taken, and complete the

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EXAMPLES FOR PRACTICE

In Adfected Quadratics of one unknown quantity.

1. Given x2+2x=15, to find the values of x. Ans. x=3, or

2. Given x2+6x=40, to find the values of x.

-5.

Ans. x=4, or -19

3. Given 4x2-8x=60, to find the values of x. Ans. x=5, or

4. Given y2-y=30, to find the values of y. Ans. y=6, or -5

I

5. Given y-y=6, to find the value of y.

Ans. y=9.

6. Given y-y=14, to find the value of y.

Ans. y=16.

-2y2=7+1⁄2√ÿ, to find the value of

7. Given y+2y

y.

Ans. y=4.

8. Given 3x2+9x+6=36, to find the values of x.

Ans. x=2, or -5.

9. Given 4x2-x=60, to find the values of x.

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12. Given x+6x2-40, to find the values of x.

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19. Given x2-6x+2=3, to find the values of x.

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20. Given lues of x.

3x+1×/2x−1=12, to find the va

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23. Given x-6x=27, to find the values of x.

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24. Given 2+4x=16-, to find the values

of x.

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26. Given x2+4x+4√√x2+4x+15=45, to find the values of x.

27. Given

Ans. x-3, or -7, or 1/89-2. x-4x3+8x=165, to find the values

of x.

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Ans. x=5, or 3, or 1-10.

28. Given 6x-3x2+61/3x2-6x-8=-24, to find the values of x.

Ans. x=6, or 4, or 1±5.

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30. Given x+2x3-x=3080, to find the values of x.

Ans. x=7, or -8, or

1±√-219 2

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