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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. 106 E (page 885)

In the following exercises, solve by completing the square.
$3 x^{2} - 14 x + 8 = 0$

Short Answer

Expert verified

The solution is $x = \frac{2}{3}, x = 4$

Step by step solution

01

Step 1. Given information

Equation: $3 x^{2} - 14 x + 8 = 0$

02

Step 2. Calculation

We have,

$3 x^{2} - 14 x + 8 = 0$

localid="1645178760253" $3 x^{2} - 14 x + 8 - 8 = 0 - 8$

$\frac{3 x^{2} - 14 x}{3} = \frac{- 8}{3}$

$x^{2} - \frac{14 x}{3} = \frac{- 8}{3}$

localid="1645178864584" $x^{2} - \frac{14 x}{3} + {(\frac{1}{2} 路 (- \frac{14}{3}))}^{2} = \frac{- 8}{3} + {(\frac{1}{2} 路 (- \frac{14}{3}))}^{2}$

localid="1645178889066" $x^{2} - \frac{14 x}{3} + {(\frac{- 7}{3})}^{2} = \frac{- 8}{3} + {(\frac{- 7}{3})}^{2}$

localid="1645179042680" $x^{2} - \frac{14 x}{3} + \frac{49}{9} = \frac{- 8}{3} + \frac{49}{9}$

localid="1645179082190" ${(x - \frac{7}{3})}^{2} = \frac{25}{9}$

$\sqrt{{(x - \frac{7}{3})}^{2}} = \sqrt{\frac{25}{9}}$

localid="1645179299091" $x - \frac{7}{3} = 卤 \frac{5}{3}$

$x - \frac{7}{3} + \frac{7}{3} = - \frac{5}{3} + \frac{7}{3}, x - \frac{7}{3} + \frac{7}{3} = \frac{5}{3} + \frac{7}{3}$

localid="1645179204367" $x = \frac{2}{3}, x = 4$

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