martinezadam576
Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Select the correct answer.

What are the solutions to this equation?

[tex]\[ 16x^2 + 9 = 25 \][/tex]

A. [tex]\( x = -4 \)[/tex] and [tex]\( x = 4 \)[/tex]

B. [tex]\( x = 0 \)[/tex] and [tex]\( x = 4 \)[/tex]

C. [tex]\( x = 0 \)[/tex] and [tex]\( x = 1 \)[/tex]

D. [tex]\( x = -1 \)[/tex] and [tex]\( x = 1 \)[/tex]

Sagot :

GinnyAnswer
Let's solve the equation step by step:

The given equation is:
[tex]\[ 16x^2 + 9 = 25 \][/tex]

First, we move the constant term on the right side to the left side by subtracting 25 from both sides of the equation:
[tex]\[ 16x^2 + 9 - 25 = 0 \][/tex]
[tex]\[ 16x^2 - 16 = 0 \][/tex]

Next, simplify the equation:
[tex]\[ 16x^2 - 16 = 0 \][/tex]

Factor out the common factor on the left-hand side:
[tex]\[ 16(x^2 - 1) = 0 \][/tex]

Now, set each factor equal to zero:
[tex]\[ x^2 - 1 = 0 \][/tex]

To solve for [tex]\( x \)[/tex], we move the constant term to the right side:
[tex]\[ x^2 = 1 \][/tex]

Taking the square root of both sides gives:
[tex]\[ x = \pm 1 \][/tex]

This means the solutions to the equation are:
[tex]\[ x = -1 \][/tex]
and
[tex]\[ x = 1 \][/tex]

Based on these solutions, the correct answer is:
D. [tex]\( x = -1 \)[/tex] and [tex]\( x = 1 \)[/tex]
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.