Question

Evaluating Substituted Values of x
x Substituted Evaluate True Statement?
7−11−−√

7
11−7–√

7+11−−√

11+7–√

For the quadratic equation (x−7)2=11
, complete the table by testing each of the given values to determine whether it is a solution. Identify the two solutions to the quadratic equation.

Answer 1

I'll test each x by computing (x − 7)^2 and checking whether it equals 11.

- x = 7 − √11
- (x − 7)^2 = (7 − √11 − 7)^2 = (−√11)^2 = 11 → True (solution).

- x = 7
- (x − 7)^2 = 0^2 = 0 ≠ 11 → Not a solution.

- x = √11 − 7
- (x − 7)^2 = (√11 − 7 − 7)^2 = (√11 − 14)^2 ≠ 11 (numerically ≈ 114.17) → Not a solution.

- x = 7 + √11
- (x − 7)^2 = (7 + √11 − 7)^2 = (√11)^2 = 11 → True (solution).

- x = √11 + 7
- This is the same as 7 + √11, so it is a solution.

The two distinct solutions are x = 7 ± √11 (i.e., 7 + √11 and 7 − √11).