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Answer :
To solve the equation [tex]\(9x^2 = 17\)[/tex], you can follow these steps:
1. Isolate [tex]\(x^2\)[/tex]:
Divide both sides of the equation by 9 to solve for [tex]\(x^2\)[/tex].
[tex]\[
x^2 = \frac{17}{9}
\][/tex]
2. Take the square root of both sides:
To solve for [tex]\(x\)[/tex], take the square root of both sides of the equation. Remember to consider both the positive and negative square roots.
[tex]\[
x = \sqrt{\frac{17}{9}} \quad \text{and} \quad x = -\sqrt{\frac{17}{9}}
\][/tex]
3. Simplify the square root:
The square root of a fraction can be simplified as the square root of the numerator over the square root of the denominator.
[tex]\[
x = \frac{\sqrt{17}}{\sqrt{9}} \quad \text{and} \quad x = -\frac{\sqrt{17}}{\sqrt{9}}
\][/tex]
Since [tex]\(\sqrt{9} = 3\)[/tex], this becomes:
[tex]\[
x = \frac{\sqrt{17}}{3} \quad \text{and} \quad x = -\frac{\sqrt{17}}{3}
\][/tex]
4. Calculate and round to the nearest hundredth:
By calculating [tex]\(\frac{\sqrt{17}}{3}\)[/tex], we find:
[tex]\[
x \approx 1.37 \quad \text{and} \quad x \approx -1.37
\][/tex]
Therefore, the solutions to the equation [tex]\(9x^2 = 17\)[/tex] are approximately [tex]\(1.37\)[/tex] and [tex]\(-1.37\)[/tex], rounded to the nearest hundredth.
1. Isolate [tex]\(x^2\)[/tex]:
Divide both sides of the equation by 9 to solve for [tex]\(x^2\)[/tex].
[tex]\[
x^2 = \frac{17}{9}
\][/tex]
2. Take the square root of both sides:
To solve for [tex]\(x\)[/tex], take the square root of both sides of the equation. Remember to consider both the positive and negative square roots.
[tex]\[
x = \sqrt{\frac{17}{9}} \quad \text{and} \quad x = -\sqrt{\frac{17}{9}}
\][/tex]
3. Simplify the square root:
The square root of a fraction can be simplified as the square root of the numerator over the square root of the denominator.
[tex]\[
x = \frac{\sqrt{17}}{\sqrt{9}} \quad \text{and} \quad x = -\frac{\sqrt{17}}{\sqrt{9}}
\][/tex]
Since [tex]\(\sqrt{9} = 3\)[/tex], this becomes:
[tex]\[
x = \frac{\sqrt{17}}{3} \quad \text{and} \quad x = -\frac{\sqrt{17}}{3}
\][/tex]
4. Calculate and round to the nearest hundredth:
By calculating [tex]\(\frac{\sqrt{17}}{3}\)[/tex], we find:
[tex]\[
x \approx 1.37 \quad \text{and} \quad x \approx -1.37
\][/tex]
Therefore, the solutions to the equation [tex]\(9x^2 = 17\)[/tex] are approximately [tex]\(1.37\)[/tex] and [tex]\(-1.37\)[/tex], rounded to the nearest hundredth.
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