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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 7: Q. 7.156 (page 887)

Solve: $16 y^{2} = 32 y^{3} + 2 y$

Short Answer

Expert verified

The answer is $y = 0, \frac{1}{4}, \frac{1}{4}$

Step by step solution

01

Step 1. Given Information.

The given equation is $16 y^{2} = 32 y^{3} + 2 y$ .

02

Step 2. Factors of the equation.

Bring all the terms to one side:

$32 y^{3} - 16 y^{2} + 2 y = 0$

Factor the greatest common factor,

$2 y (16 y^{2} - 8 y + 1) = 0$

Now, Factor the trinomial,

$2 y (16 y^{2} - 4 y - 4 y + 1) = 0 2 y {4 y (4 y - 1) - 1 (4 y - 1)} = 0 2 y (4 y - 1) (4 y - 1) = 0$

03

Step 3. Solution of the equation.

On solving,

$2 y = 0, 4 y - 1 = 0, 4 y - 1 = 0 y = 0, y = \frac{1}{4}, y = \frac{1}{4}$

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