Question

Solve the equation 6, x, squared, plus, 1, equals, 10, x6x
2
+1=10x to the nearest tenth.

Answer 1

To solve the equation \(6x^2 + 1 = 10\), we start by isolating the variable term.

1. First, subtract 1 from both sides:
\[
6x^2 = 10 - 1
\]
\[
6x^2 = 9
\]

2. Next, divide both sides by 6:
\[
x^2 = \frac{9}{6}
\]
\[
x^2 = \frac{3}{2}
\]

3. To find \(x\), take the square root of both sides:
\[
x = \pm \sqrt{\frac{3}{2}}
\]

4. Simplifying \(\sqrt{\frac{3}{2}}\):
\[
x = \pm \frac{\sqrt{3}}{\sqrt{2}} = \pm \frac{\sqrt{6}}{2}
\]

5. Now we compute the approximate values of \(x\):
\(\sqrt{6} \approx 2.449\), so:
\[
x \approx \pm \frac{2.449}{2} \approx \pm 1.2245
\]

6. Rounding to the nearest tenth, we have:
\[
x \approx \pm 1.2
\]

Thus, the solutions to the equation \(6x^2 + 1 = 10\) are approximately \(1.2\) and \(-1.2\).