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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. 532 (page 988)

Solve the following quadratic equations. Use any method.
$2 x (3 x - 2) - 1 = 0$

Short Answer

Expert verified

The required solution is:

$x = \frac{2 + \sqrt{10}}{6}, 鈥� x = \frac{2 - \sqrt{10}}{6}$

Step by step solution

01

Step 1. Given information.

We have:

$2 x (3 x - 2) - 1 = 0$

02

Step 2. Make a standard form of quadratic equation.

$2 x (3 x - 2) - 1 = 0$

Apply distributive law: $a (b - c) = a b - a c$

$2 x 路鈥� 3 x - 2 x 路鈥� 2 - 1 = 0 6 x^{2} - 4 x - 1 = 0$

03

Step 3. Solve the quadratic equation.

For a quadratic equation of the standard form, the solutions are:

$a x^{2} + b x + c = 0 鈥� x_{1, 鈥� 2} = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a} For 鈥� a = 6, 鈥� b = - 4, 鈥� c = - 1 x_{1, 鈥� 2} = \frac{- (- 4) 卤 \sqrt{{(- 4)}^{2} - 4 路鈥� 6 (- 1)}}{2 路鈥� 6} x_{1, 鈥� 2} = \frac{- (- 4) 卤鈥� 2 \sqrt{10}}{2 路鈥� 6} x = \frac{2 + \sqrt{10}}{6}, 鈥� x = \frac{2 - \sqrt{10}}{6}$

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Most popular questions from this chapter

In the following exercises, solve by using the Quadratic Formula.
$y^{2} + 4 y - 4 = 0$

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

$a) b^{2} + 7 b - 13 = 0 b) 5 a^{2} - 6 a + 10 = 0 c) 4 r^{2} - 20 r + 25 = 0$

An arrow is shot vertically upward at a rate of 220 feet per second. Use the projectile formula $h = - 16 t^{2} + v_{o} t$ , to determine when height of the arrow will be 400 feet.

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

Solve by using the Quadratic Formula: $3 y^{2} - 5 y + 2 = 0$

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