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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. 4 (page 869)

Solve Quadratic Equations of the Form $a x^{2} = k$ Using the Square Root Property.
In the following exercises, solve each equation $t^{2} - 75 = 0$

Short Answer

Expert verified

The solution of the quadratic equation: $t = 5 \sqrt{3}, t = - 5 \sqrt{3}$

Step by step solution

01

Given information

Consider the quadratic equation $t^{2} - 75 = 0$

The objective is to solve the quadratic equation by using the square root property.

If $x^{2} = k$ , then $x = 卤 \sqrt{k}$

Isolate the quadratic term and make its coefficient one. Add 75 to both sides.

$t^{2} = 75$

02

Apply square root property

So, $t = 卤 \sqrt{75}$

Simplify the radical.

$t = 卤 \sqrt{25 路 3} t = 卤 5 \sqrt{3}$

Rewrite to show two solutions.

$t = 5 \sqrt{3}, t = - 5 \sqrt{3}$

03

Step 3. Check the solutions

Substitute $t = 5 \sqrt{3}$ in the original equation.

role="math" localid="1645624945088" $t^{2} - 75 = 0 {(5 \sqrt{3})}^{2} - 75 \overset{?}{=} 0 75 - 75 = 0 0 = 0$

Substitute $t = - 5 \sqrt{3}$ in the original equation.

$t^{2} - 75 = 0 {(- 5 \sqrt{3})}^{2} - 75 \overset{?}{=} 0 75 - 75 = 0 0 = 0$

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Most popular questions from this chapter

In the following exercises, solve by using the Quadratic Formula: $q^{2} + 3 q - 18 = 0$

The product of two consecutive even integers is 168. Find the integers.

Find the base and height of a triangle whose base is four inches more than six times its height and has an area of 456 square inches.

Solve :- $x^{4} - 11 x^{2} + 28 = 0$

Determine the number and type of solutions to each quadratic equation.

$a) 8 m^{2} - 3 m + 6 = 0 b) 5 z^{2} + 6 z - 2 = 0 c) 9 w^{2} + 24 w + 16 = 0$

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