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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.435. (page 983)

Solve by using the quadratic formula.
$4 x^{2} - 5 x + 1 = 0$

Short Answer

Expert verified

The solution is $x = 1$ and $x = \frac{1}{4}$ .

Step by step solution

01

Step 1. Given information.

The given equation is $4 x^{2} - 5 x + 1 = 0$ .

02

Step 2. Write the equation in standard form.

The standard form of the quadratic equation is $a x^{2} + b x + c = 0$ .

$4 x^{2} - 5 x + 1 = 4 x^{2} + (- 5) x + 1$

So, here $a = 4, b = - 5, c = 1$ .

03

Step 3. Apply the quadratic formula.

The quadratic formula is $x = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a}$ .

$\begin{array}{rcl} x & = & \frac{- (- 5) 卤 \sqrt{{(- 5)}^{2} - 4 脳 4 脳 1}}{2 (4)} \\ x & = & \frac{5 卤 \sqrt{25 - 16}}{8} \\ x & = & \frac{5 卤 \sqrt{9}}{8} \\ x & = & \frac{5 卤 3}{8} \end{array}$

04

Step 5. Now solve the equation for x.

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

05

Step 5. Simplified answer.

Hence, the required solution is $x = 1$ and $x = \frac{1}{4}$ .

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