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Answer :
Sure! Let's go through the steps to solve the equation [tex]\(x^2 = 50\)[/tex] and find the value of [tex]\(x\)[/tex].
1. Understand the Goal: We need to find the value of [tex]\(x\)[/tex] such that when it's squared, it equals 50.
2. Apply Square Root: The equation [tex]\(x^2 = 50\)[/tex] can be solved by taking the square root of both sides. This will help us find the values of [tex]\(x\)[/tex].
3. Consider Positive and Negative Roots: When you take the square root of a number, you get two possible values: both positive and negative. This is because both [tex]\((+x)\)[/tex] and [tex]\((-x)\)[/tex] squared give the same positive result. So, we have:
[tex]\[
x = \pm \sqrt{50}
\][/tex]
4. Simplify the Square Root:
The square root of 50 can be simplified if needed, but for finding an approximate value, we calculate:
[tex]\[
\sqrt{50} \approx 7.071
\][/tex]
5. Write the Final Values: Considering both the positive and negative roots, the two possible values for [tex]\(x\)[/tex] are approximately:
[tex]\[
x = 7.071 \quad \text{and} \quad x = -7.071
\][/tex]
Therefore, the solution that matches those approximate values from the given options is [tex]\(\pm \sqrt{50}\)[/tex]. So, the value of [tex]\(x\)[/tex] can be expressed as [tex]\(\pm \sqrt{50}\)[/tex].
1. Understand the Goal: We need to find the value of [tex]\(x\)[/tex] such that when it's squared, it equals 50.
2. Apply Square Root: The equation [tex]\(x^2 = 50\)[/tex] can be solved by taking the square root of both sides. This will help us find the values of [tex]\(x\)[/tex].
3. Consider Positive and Negative Roots: When you take the square root of a number, you get two possible values: both positive and negative. This is because both [tex]\((+x)\)[/tex] and [tex]\((-x)\)[/tex] squared give the same positive result. So, we have:
[tex]\[
x = \pm \sqrt{50}
\][/tex]
4. Simplify the Square Root:
The square root of 50 can be simplified if needed, but for finding an approximate value, we calculate:
[tex]\[
\sqrt{50} \approx 7.071
\][/tex]
5. Write the Final Values: Considering both the positive and negative roots, the two possible values for [tex]\(x\)[/tex] are approximately:
[tex]\[
x = 7.071 \quad \text{and} \quad x = -7.071
\][/tex]
Therefore, the solution that matches those approximate values from the given options is [tex]\(\pm \sqrt{50}\)[/tex]. So, the value of [tex]\(x\)[/tex] can be expressed as [tex]\(\pm \sqrt{50}\)[/tex].
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