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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. 9.52 (page 894)

Solve by using the Quadratic Formula: $\frac{1}{9} d^{2} - \frac{1}{2} d = - \frac{1}{3}$

Short Answer

Expert verified

The solution of the quadratic equation is $d = \frac{9 卤 \sqrt{33}}{4}$

Step by step solution

01

Given information

We are given a quadratic equation $\frac{1}{9} d^{2} - \frac{1}{2} d = - \frac{1}{3}$

02

Multiply BY LCD and simplify

we get

$18 (\frac{1}{9} d^{2} - \frac{1}{2} d) = 18 (- \frac{1}{3}) 2 d^{2} - 9 d = - 6$

03

Add 6 on both sides and identify the values of a,b,c

We get,

$2 d^{2} - 9 d + 6 = 0$

On comparing with standard equation we get $a = 2, b = - 9, c = 6$

04

Write quadratic formula and substitute the values in it

The quadratic formula can be given as

$d = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a}$

On substituting the values we get

$d = \frac{9 卤 \sqrt{81 - 4 (2) (6)}}{2 (2)}$

05

Simplify

We have,

$d = \frac{9 卤 \sqrt{81 - 48}}{4} d = \frac{9 卤 \sqrt{33}}{4}$

06

Conclusion

The solution of the quadratic equation is $d = \frac{9 卤 \sqrt{33}}{4}$

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Most popular questions from this chapter

The product of two consecutive even integers is 168. Find the integers.

Solve :- $x - 7 \sqrt{x} + 12 = 0$

Determine the number and type of solutions to each quadratic equation.

$a) 8 m^{2} - 3 m + 6 = 0 b) 5 z^{2} + 6 z - 2 = 0 c) 9 w^{2} + 24 w + 16 = 0$

In the following exercises, solve by using the Quadratic Formula.
$(x + 1) (x - 3) = 2$

In the following exercises, solve by using the Quadratic Formula.
$\frac{1}{9} c^{2} + \frac{2}{3} c = 3$

See all solutions

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