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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. 100 E (page 885)

In the following exercises, solve by completing the square.
$2 x^{2} - 14 x + 12 = 0$

Short Answer

Expert verified

The solution is $x = 1, x = 6$ .

Step by step solution

01

Step 1. Given information

Equation: $2 x^{2} - 14 x + 12 = 0$

02

Step 2. Calculation

We have,

$2 x^{2} - 14 x + 12 = 0$

$2 (x^{2} - 7 x + 6) = 0$

$\frac{2 (x^{2} - 7 x + 6)}{2} = \frac{0}{2}$

$x^{2} - 7 x + 6 = 0$

$x^{2} - 7 x + 6 - 6 = 0 - 6$

$x^{2} - 7 x + {(\frac{1}{2} 路 (- 7))}^{2} = - 6 + {(\frac{1}{2} 路 (- 7))}^{2}$

$x^{2} - 7 x + {(\frac{- 7}{2})}^{2} = - 6 + {(\frac{- 7}{2})}^{2}$

$x^{2} - 7 x + \frac{49}{4} = - 6 + \frac{49}{4}$

${(x - \frac{7}{2})}^{2} = \frac{25}{4}$

$\sqrt{{(x - \frac{7}{2})}^{2}} = \sqrt{\frac{25}{4}}$

$x - \frac{7}{2} = 卤 \frac{5}{2}$

$x - \frac{7}{2} + \frac{7}{2} = - \frac{5}{2} + \frac{7}{2}, x - \frac{7}{2} + \frac{7}{2} = \frac{5}{2} + \frac{7}{2}$

$x = \frac{2}{2}, x = \frac{12}{2}$

$x = 1, x = 6$

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