Question

Use the table to answer the 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.

Note: The solutions in the table are arranged from the smallest number at the top to the largest number at the bottom.

(1 point)
The smaller of the two solutions is x=

. The larger of the two solutions is x=

.

Answer 1

The solutions are x = 7 ± √11.

So the smaller solution is x = 7 − √11 and the larger is x = 7 + √11 (≈ 3.683 and 10.317).