Use the table to answer the question.
x Substituted Evaluate True Statement?
7−11−−√
7
−
11
7
11−7–√
11
−
7
7+11−−√
7
+
11
11+7–√
11
+
7
For the quadratic equation (x−7)2=11
(
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.
(1 point)
The smaller of the two solutions is x=
x
=
. The larger of the two solutions is x=
x
=
.
To test each value, we substitute it into the equation and see if it makes a true statement.
For x = 7 - √11:
(7 - √11 - 7)^2 = 11
(-√11)^2 = 11
11 = 11
This is a true statement.
For x = 7 + √11:
(7 + √11 - 7)^2 = 11
(√11)^2 = 11
11 = 11
This is also a true statement.
Therefore, both x = 7 - √11 and x = 7 + √11 are solutions to the quadratic equation (x - 7)^2 = 11.