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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. 9.39 TI (page 884)

Solve by completing the square :
$4 x^{2} + 3 x = 2$

Short Answer

Expert verified

The required value of $x$ is $\frac{- 3 + \sqrt{41}}{8}, \frac{- 3 - \sqrt{41}}{8}$

Step by step solution

01

Given information

$4 x^{2} + 3 x = 2$

02

Calculation

$4 x^{2} + 3 x = 2 鈬� \frac{4 x^{2} + 3 x}{4} = \frac{2}{4} 鈬� x^{2} + \frac{3}{4} x = \frac{1}{2} 鈬� x^{2} + \frac{3}{4} x + {(\frac{1}{2} 脳 \frac{3}{4})}^{2} = \frac{1}{2} 鈬� x^{2} + \frac{3}{4} x + \frac{9}{64} = \frac{1}{2} + \frac{9}{64} 鈬� {(x + \frac{3}{8})}^{2} = \frac{41}{64} 鈬� x + \frac{3}{8} = 卤 \sqrt{\frac{41}{64}} 鈬� x = - \frac{3}{8} 卤 \frac{\sqrt{41}}{8} = \frac{- 3 + \sqrt{41}}{8}, \frac{- 3 - \sqrt{41}}{8}$

The required value of $x$ is $\frac{- 3 + \sqrt{41}}{8}, \frac{- 3 - \sqrt{41}}{8}$

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Most popular questions from this chapter

Solve quadratic equation $25 x^{2} - 30 x + 9 = 36$ using square root property

In the following exercises, solve by using the Quadratic Formula.
$\frac{1}{3} n^{2} + n = - \frac{1}{2}$

Use the Discriminant to Predict the Number of Solutions of a Quadratic Equation.

In the following exercises, determine the number of solutions for each quadratic equation.

$(a) 9 v^{2} - 15 v + 25 = 0 (b) 100 w^{2} + 60 w + 9 = 0 (c) 5 c^{2} + 7 c - 10 = 0$

Solve by using the Quadratic Formula: $r^{2} + 10 r + 25 = 0$

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