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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 10: Q 124 (page 1195)

Solve the equation using quadratic formula.
$3 t (t - 2) = 2$

Short Answer

Expert verified

The roots are $t = \frac{3 + \sqrt{15}}{3}, t = \frac{3 - \sqrt{15}}{3}$ .

Step by step solution

01

Given Information.

The given equation is $3 t (t - 2) = 2$ .

02

Write the quadratic equation in standard form and identify a,b,c.

$3 t (t - 2) = 2$

Use distributive property.

$3 t^{2} - 6 t = 2 3 t^{2} - 6 t - 2 = 0$

Here,

$a = 3, b = - 6, c = - 2$

03

Substitute the values in quadratic formula.

$t = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a} t = \frac{- (- 6) 卤 \sqrt{(- 6)^{2} - 4 (3) (- 2)}}{2 (3)} t = \frac{6 卤 \sqrt{36 + 24}}{6} t = \frac{6 卤 \sqrt{60}}{6}$

04

Use square root property.

$t = \frac{6 卤 2 \sqrt{15}}{6} t = \frac{3 卤 \sqrt{15}}{3}$

Rewrite to show two solutions.

$t = \frac{3 + \sqrt{15}}{3}, t = \frac{3 - \sqrt{15}}{3}$

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Most popular questions from this chapter

Solve the quadratic equation using square root property.

${(t - \frac{5}{6})}^{2} = \frac{11}{25}$

Solve the quadratic equation using square root property.

$(a - 4)^{2} = 28$

Complete the square to make a perfect square trinomial. Write the result as a binomial square.

$p^{2} + \frac{1}{4} p$

Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared.

$x^{2} - 9 x$

The product of two consecutive odd integers is 99. Find the integers.

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