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nydus/The First Steps in AlgebraPublic

Page 139 of 227

Table of Contents

Pure Quadratic Equations.

Exercise 71.

Solve:

$5 x^{2} - 2 = 3 x^{2} + 6$ .

$3 x^{2} + 1 = 2 x^{2} + 10$ .

$4 x^{2} - 50 = x^{2} + 25$ .

$(x - 6) (x + 6) = 28$ .

$(x - 5) (x + 5) = 24$ .

$3 (x^{2} - 11) + 2 (x^{2} - 5) = 82$ .

$11 (x^{2} + 5) + 6 (3 - x^{2}) = 198$ .

$5 x^{2} + 3 - 2 (17 - x^{2}) = 32$ .

$4 (x + 1) - 4 (x - 1) = x^{2} - 1$ .

$86 - 52 x = 2 (8 - x) (2 - 3 x)$ .

Find two numbers that are to each other as $3$ to $4$ , and the difference of whose squares is $112$ .

Let $3 x$ stand for the smaller and $4 x$ for the larger number.

A boy bought a number of oranges for $36$ cents. The price of an orange was to the number bought as $1$ to $4$ . How many oranges did he buy, and how many cents did each orange cost?

A certain street contains $144$ square rods, and the length is $16$ times the width. Find the width.

Find the number of rods in the length, and in the width of a rectangular field containing $3 \frac{3}{5}$ acres, if the length is $4$ times the width.

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