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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.9.19 (page 868)

Solve $9 m^{2} - 12 m + 4 = 25$

Short Answer

Expert verified

The solutions of the quadratic equation: $m = \frac{7}{3}, m = - 1$

Step by step solution

01

Step 1. Given information

Consider the quadratic equation

$9 m^{2} - 12 m + 4 = 25$

Factor the perfect square trinomial.

${(3 m - 2)}^{2} = 25$

Use the Square Root Property.

$3 m - 2 = 卤 \sqrt{25} 3 m - 2 = 卤 5$

Add 2 to both sides.

$3 m = 卤 5 + 2$

Solve for $m$ .

localid="1645462854035" $m = \frac{卤 5 + 2}{3}$

Rewrite to show two solutions.

$m = \frac{5 + 2}{3}, m = \frac{- 5 + 2}{3} m = \frac{7}{3}, m = - 1$

02

Step 2. Check for solutions.

Substitute $m = \frac{7}{3}$ in the original equation.

$9 m^{2} - 12 m + 4 = 25 9 {(\frac{7}{3})}^{2} - 12 (\frac{7}{3}) + 4 \overset{?}{=} 25 9 (\frac{49}{9}) - 28 + 4 \overset{?}{=} 25 49 - 28 + 4 \overset{?}{=} 25 25 = 25$

Substitute $m = - 1$ in the original equation.

localid="1645463312302" $9 m^{2} - 12 m + 4 = 25 9 {(- 1)}^{2} - 12 (- 1) + 4 \overset{?}{=} 25 9 + 12 + 4 \overset{?}{=} 25 25 = 25$

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Most popular questions from this chapter

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