Q.429. Solve by completing the square.4... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q.429. (page 983)

Solve by completing the square.
$4 y^{2} - 6 y = 4$

Short Answer

Expert verified

The solution is $y = 2$ and $y = - \frac{1}{2}$ .

Step by step solution

Step 1. Given information.

The given equation is $4 y^{2} - 6 y = 4$ .

Step 2. First, isolate the variable and constant terms on one side.

$\begin{array}{rcl} 4 y^{2} - 6 y & = & 4 \\ \frac{4 y^{2}}{4} - \frac{6}{4} y & = & \frac{4}{4} \\ y^{2} - \frac{3}{2} y & = & 1 \end{array}$

Step 3. Simplify the equation.

$\begin{array}{rcl} y^{2} - \frac{3}{2} y & = & 1 \\ y^{2} - 2 路 y 路 \frac{3}{4} & = & 1 \\ y^{2} - 2 路 y 路 \frac{3}{4} + \frac{9}{16} & = & 1 + \frac{9}{16} 鈰� 鈰� (a d d \frac{9}{16} o n b o t h s i d e s) \\ y^{2} - 2 路 y 路 \frac{3}{4} + {(\frac{3}{4})}^{2} & = & \frac{25}{16} \\ {(y - \frac{3}{4})}^{2} & = & \frac{25}{16} \\ y - \frac{3}{4} & = & 卤 \sqrt{\frac{25}{16}} \\ y - \frac{3}{4} & = & 卤 \frac{5}{4} \end{array}$

Step 4. Solve the equation for y.

$\begin{array}{rcl} y - \frac{3}{4} & = & \frac{5}{4} \\ y & = & \frac{5}{4} + \frac{3}{4} \\ y & = & \frac{8}{4} \\ y & = & 2 \end{array}$ and $\begin{array}{rcl} y - \frac{3}{4} & = & - \frac{5}{4} \\ y & = & - \frac{5}{4} + \frac{3}{4} \\ y & = & \frac{- 5 + 3}{4} \\ y & = & - \frac{2}{4} \\ y & = & - \frac{1}{2} \end{array}$

Step 5. Simplified answer.

Hence, the required solution is $y = 2$ and $y = - \frac{1}{2}$ .

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91影视

Solve by completing the square.
$4 y^{2} - 6 y = 4$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. First, isolate the variable and constant terms on one side.

Step 3. Simplify the equation.

Step 4. Solve the equation for y.

Step 5. Simplified answer.

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91影视

Solve by completing the square.4y2-6y=4

Short Answer

Step by step solution

Step 1. Given information.

Step 2. First, isolate the variable and constant terms on one side.

Step 3. Simplify the equation.

Step 4. Solve the equation for y.

Step 5. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Applied Mathematics

Statistics

Discrete Mathematics

Geometry

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve by completing the square.
$4 y^{2} - 6 y = 4$