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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 90 E (page 1069)

Solve quadratic equations of the form $x^{2} + b x + c = 0$ by completing the square.
In the following exercises, solve by completing the square.
$t^{2} - 10 t - 6 = 5$

Short Answer

Expert verified

The required value of $t$ is $11, - 1$

Step by step solution

01

Given information

$t^{2} - 10 t - 6 = 5$

02

Calculation

$t^{2} - 10 t - 6 = 5 鈬� t^{2} - 10 t = 5 + 6 鈬� t^{2} - 10 t = 11 鈬� t^{2} - 10 t + (\frac{1}{2} 脳 {(- 10))}^{2} = 11 + 25 鈬� t^{2} - 10 t + 25 = 11 + 25 鈬� {(t - 5)}^{2} = 36 鈬� t - 5 = 卤 \sqrt{36} = 卤 6 鈬� t = 5 卤 6 = 5 + 6, 5 - 6 = 11, - 1$

The required value of $t$ is $11, - 1$

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Most popular questions from this chapter

In the following exercises, simplify each expression using the properties for exponents.

$鈸� q^{27} 路 q^{15} 鈸� 5^{x} 路 5^{4 x} 鈸� 9 u^{41} 路 7 u^{53} 鈸� c^{5} 路 c^{11} 路 c^{2}$

Factor completely, $5 x^{3} + 15 x^{2} - 20 x$

In the following exercises, simplify using absolute value signs as needed. $\sqrt{n^{21}}, \sqrt[3]{q^{8}}, \sqrt[8]{n^{10}}$

In the following exercises, factor each trinomial of the form $x^{2} + b x + c$ .

$w^{2} + 10 x + 21$ .

In the following exercises, simplify using absolute value signs as needed.

$a . 8 + \sqrt{96} b . \frac{8 鈭� \sqrt{80}}{4}$

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