Chapter 9: Q. 1 (page 869)

Solve Quadratic Equations of the Form $a x^{2} = k$ Using the Square Root Property.
In the following exercises, solve each equation $a^{2} = 49$

Short Answer

Expert verified

The solution of the quadratic equation:

$a = 7, a = - 7$

Step by step solution

Given information

Consider the quadratic equation $a^{2} = 49$

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

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

So, $a = \pm \sqrt{49}$

Simplify the radical.

$a = \pm \sqrt{7 \cdot 7} a = \pm 7$

Rewrite to show two solutions.

$a = 7, a = - 7$

Check the solutions

Substitute $a = 7$ in the original equation.

$a^{2} = 49 {(7)}^{2} \overset{?}{=} 49 49 = 49$

Substitute role="math" localid="1645617109232" $a = - 7$ in the original equation.

$a^{2} = 49 {(- 7)}^{2} \overset{?}{=} 49 49 = 49$

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Solve Quadratic Equations of the Form $a x^{2} = k$ Using the Square Root Property.
In the following exercises, solve each equation $a^{2} = 49$

Short Answer

Step by step solution

Given information

Check the solutions

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Solve Quadratic Equations of the Form ax2=kUsing the Square Root Property.In the following exercises, solve each equationa2=49

Short Answer

Step by step solution

Given information

Check the solutions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Calculus

Applied Mathematics

Decision Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve Quadratic Equations of the Form $a x^{2} = k$ Using the Square Root Property.
In the following exercises, solve each equation $a^{2} = 49$