To solve the quadratic equation \((x - 7)^2 - 94 = 0\), we can follow these steps:
-
Isolate the squared term: \[ (x - 7)^2 = 94 \]
-
Take the square root of both sides: \[ x - 7 = \pm \sqrt{94} \]
-
Solve for \(x\): First, compute \(\sqrt{94}\). The square root of \(94\) is approximately \(9.695\).
Therefore, we have: \[ x - 7 = 9.695 \quad \text{or} \quad x - 7 = -9.695 \]
Solving these two equations:
- For \(x - 7 = 9.695\): \[ x = 9.695 + 7 \approx 16.695 \]
- For \(x - 7 = -9.695\): \[ x = -9.695 + 7 \approx -2.695 \]
Thus, the approximate solutions to the equation are \(x \approx 16.695\) and \(x \approx -2.695\).
Since these values are not close to any options given in your responses, I may have made an error in approximating \(\sqrt{94}\).
Let’s check these solutions more accurately.
Calculating \(\sqrt{94}\) explicitly gives us \(y = 9.695\).
Adding/subtracting the exact value:
- \(x = 7 + \sqrt{94}\)
- \(x = 7 - \sqrt{94}\)
This implies:
- First solution: \(x \approx 7 + 9.695 \approx 16.695\) (not in available answers)
- Second solution: \(x \approx 7 - 9.695 \approx -2.695\) (not in available answers)
Given these calculations do not directly fit the choices presented, we can further evaluate if either of these match an estimated calculation from the responses, yet none directly correlate I approximate evaluations.
Upon reevaluating possible miscalculations with square roots yielding non-integers and returning toward integer forms leads me to suggest the best provision could be through different alternate methods.
Overall, the solution set from evident integers directly suggests:
- Evaluate \( \sqrt{94} \) near \(9.7\), leading to potential revisions if summing up even closest integers doesn't partake alignments to the functions required.
Hence, we conclude numerically while none of the provided sets align perfectly unless set conversely yielding fractions from original rounds. The equivalent assessment of direct solutions reflect proper selections.
If more clarity is sought or retrials are necessary encompassing those integers, do revert into distinct flowering probe through discussions.
1 answer