To solve the quadratic equation \(2x^2 - 5 = 6\), we first rearrange it into standard form by adding 5 to both sides:
\[ 2x^2 - 5 + 5 = 6 + 5 \] \[ 2x^2 = 11 \]
Next, we divide both sides by 2:
\[ x^2 = \frac{11}{2} \]
Now we take the square root of both sides:
\[ x = \pm \sqrt{\frac{11}{2}} = \pm \frac{\sqrt{11}}{\sqrt{2}} = \pm \frac{\sqrt{22}}{2} \]
We can approximate \(\sqrt{22}\) using a calculator:
\[ \sqrt{22} \approx 4.690 \]
Thus,
\[ x \approx \pm \frac{4.690}{2} \approx \pm 2.345 \]
So, rounding to the nearest hundredth, we find:
\[ x \approx 2.35 \quad \text{and} \quad x \approx -2.35 \]
Now, we compare the found values with the provided options. The possible solutions are:
A. \(x=1.03\)
B. \(x=-1.03\)
C. \(x=-0.89\)
D. \(x=0.89\)
None of these options match our calculated values \(2.35\) or \(-2.35\). Thus, it seems that there might be an error in the options provided or in the quadratic expression that was given to solve.
If we assume there was an error in the presentation of the problem or are asked to simply select the closest option, it appears no answer provided is correct based on the calculated values from solving the equation \(2x^2 - 5 = 6\).
Please confirm if the equation or options might be incorrect.