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Intermediate Algebra

OPENSTAX

$Math Studyset Vaia Explanations$ Math

OER 2017 Edition · 1346 pages

ISBN: 9780998625720

Chapter 11: Q. 43 (page 1069)

Solve a quadratic equation $25 x^{2} - 30 x + 9 = 36$ using square root property

Short Answer

Expert verified

The values of $x$ are $\frac{9}{5}$ and $- \frac{3}{5}$

Step by step solution

01

Step 1. Given information

The quadratic equation $25 x^{2} - 30 x + 9 = 36$

02

Step 2. Factor the perfect square trinomial

$\Rightarrow {(5 x - 3)}^{2} = 36$

03

Step 3. Use square root property

$\Rightarrow 5 x - 3 = \pm 6$

$\Rightarrow 5 x = \pm 6 + 3$

localid="1645190460132" $\Rightarrow x = \frac{9}{5}$ andlocalid="1645190472156" $x = - \frac{3}{5}$

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Most popular questions from this chapter

In the following exercises, factor completely

$24 a^{4} - 9 a^{3}$ .

Simplify the rational expression $\frac{p^{3} + 3 p^{2} + 4 p + 12}{p^{2} + p - 6} .$

Factor Trinomials of the Form $a x^{2} + b x + c$ using the ‘ac’ Method.

$5 s^{2} - 9 s + 4$

In the following exercises, factor each trinomial of the form

$x^{2} + b x + c x^{2} - 12 - 11 x$

In the following exercises, factor the greatest common factor from each polynomial.

$- 6 a^{3} b - 12 a^{2} b^{2} + 18 a b^{2}$

See all solutions

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