Ask questions, share knowledge, and connect with a vibrant community on IDNLearn.com. Discover thorough and trustworthy answers from our community of knowledgeable professionals, tailored to meet your specific needs.
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]
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.