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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. 9.51 (page 894)

Solve by using the Quadratic Formula: $\frac{1}{4} c^{2} - \frac{1}{3} c = \frac{1}{12}$

Short Answer

Expert verified

The solution of the quadratic equation is $c = \frac{2 卤 \sqrt{7}}{3}$

Step by step solution

01

Given information

We are given a quadratic equation $\frac{1}{4} c^{2} - \frac{1}{3} c = \frac{1}{12}$

02

We multiply by LCD and simplify

We get

$12 (\frac{1}{4} c^{2} - \frac{1}{3} c) = 12 \frac{1}{12} 3 c^{2} - 4 c = 1$

03

Subtract 1 from both sides and identify the values of a,b,c

We get,

$3 c^{2} - 4 c - 1 = 0$

On comparing with standard equation we get $a = 3, b = - 4, c = - 1$

04

Write quadratic formula and substitute the values

The quadratic formula can be given given as $c = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a}$

On substituting the values we get

$c = \frac{4 卤 \sqrt{16 - 4 (3) (- 1)}}{2 (3)}$

05

Simplify

We get

$c = \frac{4 卤 \sqrt{16 + 12}}{6} c = \frac{4 卤 \sqrt{28}}{6} c = \frac{4 卤 2 \sqrt{7}}{6}$

06

Take out and remove the common factor

We have,

$c = \frac{4 卤 2 \sqrt{7}}{6} c = \frac{2 (2 卤 \sqrt{7})}{6} c = \frac{2 卤 \sqrt{7}}{6}$

07

Conclusion

The solution of the above quadratic equation is $c = \frac{2 卤 \sqrt{7}}{3}$

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Most popular questions from this chapter

Solve quadratic equation $y^{2} + 12 y + 36 = 32$ using square root property

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