Use the table to answer the question. 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.
To determine whether a given value is a solution to the quadratic equation (x-7)^2=11, we need to substitute the given value into the equation and evaluate if it is true.
Let's complete the table by substituting the given values into the equation and evaluating if the statement is true:
x | Substituted Equation | Evaluate True Statement?
---------------------------------------------------------------
7-√11 | (7-√11 - 7)^2 = 11 | Maybe
11-7-√11 | (11-7-√11 - 7)^2 = 11 | Maybe
7+√11 | (7+√11 - 7)^2 = 11 | Maybe
11+7-√11 | (11+7-√11 - 7)^2 = 11 | Maybe
By substituting the given values into the equation, and evaluating if the statement is true, we cannot determine whether any of these values are solutions to the quadratic equation. Hence, from the table, there are no solutions identified to the quadratic equation (x-7)^2=11.
To test whether a given value is a solution to a quadratic equation, you need to substitute it into the equation and see if the resulting expression is true.
Given the quadratic equation (x-7)^2=11, we need to determine whether the given values in the table are solutions.
To do this, substitute each value into the equation and evaluate the expression on both sides of the equation. If the resulting expression is true, then the value is a solution; otherwise, it is not a solution.
Let's evaluate each expression in the table:
For the first row, substitute x=7-√11 into the equation:
(7-√11-7)^2 = 11
(-√11)^2 = 11 --> 11 = 11
The resulting expression is true, so x=7-√11 is a solution to the quadratic equation.
For the second row, substitute x=7+√11 into the equation:
(7+√11-7)^2 = 11
(√11)^2 = 11 --> 11 = 11
Again, the resulting expression is true, so x=7+√11 is also a solution to the quadratic equation.
Therefore, the two solutions to the quadratic equation (x-7)^2=11 are x=7-√11 and x=7+√11.
x Substituted Evaluate True Statement?
7−11−−√ -√4=2 No
7 (7-7)^2=0 Yes
11−7–√ -√4=2 No
7+11−−√ -√4≠2 No
11+7–√ -√4≠2 No
The two solutions to the quadratic equation are x=7 and x=7.