Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Select the correct answer.

Solve the following quadratic equation:

[tex]\[(x-16)^2 = 256\][/tex]

A. [tex]\(x = -32\)[/tex] and [tex]\(x = 0\)[/tex]

B. [tex]\(x = 30\)[/tex] and [tex]\(x = -4\)[/tex]

C. [tex]\(x = -30\)[/tex] and [tex]\(x = 4\)[/tex]

D. [tex]\(x = 32\)[/tex] and [tex]\(x = 0\)[/tex]

Sagot :

GinnyAnswer
To solve the quadratic equation [tex]\((x - 16)^2 = 256\)[/tex], follow these steps:

1. Take the square root of both sides:

[tex]\[ \sqrt{(x - 16)^2} = \sqrt{256} \][/tex]

2. Simplify the equation:

[tex]\[ |x - 16| = 16 \][/tex]

3. Set up the two possible equations based on the absolute value:

[tex]\[ x - 16 = 16 \quad \text{or} \quad x - 16 = -16 \][/tex]

4. Solve each equation separately:

- For [tex]\(x - 16 = 16\)[/tex]:
[tex]\[ x - 16 = 16 \][/tex]
[tex]\[ x = 16 + 16 \][/tex]
[tex]\[ x = 32 \][/tex]

- For [tex]\(x - 16 = -16\)[/tex]:
[tex]\[ x - 16 = -16 \][/tex]
[tex]\[ x = 16 - 16 \][/tex]
[tex]\[ x = 0 \][/tex]

So, the solutions to the equation are [tex]\(x = 32\)[/tex] and [tex]\(x = 0\)[/tex], which corresponds to:

D. [tex]\(x = 32\)[/tex] and [tex]\(x = 0\)[/tex]
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.