Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
Alright, let's solve the given equation step-by-step:
The equation given is [tex]\((x - 3)^2 = 49\)[/tex].
First, we need to eliminate the square by taking the square root on both sides of the equation:
[tex]\[ \sqrt{(x - 3)^2} = \sqrt{49} \][/tex]
This results in:
[tex]\[ |x - 3| = 7 \][/tex]
The absolute value equation [tex]\(|x - 3| = 7\)[/tex] implies two possible scenarios:
1. [tex]\(x - 3 = 7\)[/tex]
2. [tex]\(x - 3 = -7\)[/tex]
Let's solve for [tex]\(x\)[/tex] in each case:
1. [tex]\(x - 3 = 7\)[/tex]
[tex]\[ x = 7 + 3 \][/tex]
[tex]\[ x = 10 \][/tex]
2. [tex]\(x - 3 = -7\)[/tex]
[tex]\[ x = -7 + 3 \][/tex]
[tex]\[ x = -4 \][/tex]
Thus, the solutions to the equation [tex]\((x - 3)^2 = 49\)[/tex] are:
[tex]\[ x = 10 \quad \text{and} \quad x = -4 \][/tex]
So, checking each option:
A. [tex]\(x = -7\)[/tex] is not a solution.
B. [tex]\(x = 10\)[/tex] is a solution.
C. [tex]\(x = 7\)[/tex] is not a solution.
D. [tex]\(x = -4\)[/tex] is a solution.
E. [tex]\(x = -10\)[/tex] is not a solution.
Therefore, the correct options are:
B. [tex]\(x = 10\)[/tex]
D. [tex]\(x = -4\)[/tex]
The equation given is [tex]\((x - 3)^2 = 49\)[/tex].
First, we need to eliminate the square by taking the square root on both sides of the equation:
[tex]\[ \sqrt{(x - 3)^2} = \sqrt{49} \][/tex]
This results in:
[tex]\[ |x - 3| = 7 \][/tex]
The absolute value equation [tex]\(|x - 3| = 7\)[/tex] implies two possible scenarios:
1. [tex]\(x - 3 = 7\)[/tex]
2. [tex]\(x - 3 = -7\)[/tex]
Let's solve for [tex]\(x\)[/tex] in each case:
1. [tex]\(x - 3 = 7\)[/tex]
[tex]\[ x = 7 + 3 \][/tex]
[tex]\[ x = 10 \][/tex]
2. [tex]\(x - 3 = -7\)[/tex]
[tex]\[ x = -7 + 3 \][/tex]
[tex]\[ x = -4 \][/tex]
Thus, the solutions to the equation [tex]\((x - 3)^2 = 49\)[/tex] are:
[tex]\[ x = 10 \quad \text{and} \quad x = -4 \][/tex]
So, checking each option:
A. [tex]\(x = -7\)[/tex] is not a solution.
B. [tex]\(x = 10\)[/tex] is a solution.
C. [tex]\(x = 7\)[/tex] is not a solution.
D. [tex]\(x = -4\)[/tex] is a solution.
E. [tex]\(x = -10\)[/tex] is not a solution.
Therefore, the correct options are:
B. [tex]\(x = 10\)[/tex]
D. [tex]\(x = -4\)[/tex]
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.