Solve the following quadratic equation using square roots: (x - 18)^2 = 196.

A) {214, -178}
B) {21, 5}
C) {-4, -32}
D) {32, 4}

1 answer

To solve the equation (x18)2=196 using square roots, we proceed as follows:

  1. Take the square root of both sides of the equation:

    x18=±196

  2. Calculate 196:

    196=14

  3. Now we have two cases to solve for x:

    • Case 1: x18=14 Solving for x: x=14+18=32

    • Case 2: x18=14 Solving for x: x=14+18=4

  4. The solutions to the equation are x=32 and x=4.

Thus, the solution set is 32,4.

The correct answer is:

D) {32, 4}.