Question

Solve the following quadratic equation using square roots: (x−18)2=196 .(1 point) Responses {21,5} left brace 21 comma 5 right brace {32,4} left brace 32 comma 4 right brace {214,−178} left brace 214 comma negative 178 right brace ​ {−4,−32}

Answer 1

To solve the quadratic equation using square roots, we can start by taking the square root of both sides of the equation:

√((x−18)²) = √196

Simplifying further, we have:

|x−18| = √196

Taking the square root of 196 gives us 14:

|x−18| = 14

Now we can set up two equations:

1. x−18 = 14
2. x−18 = -14

For the first equation, we solve for x by adding 18 to both sides:

x−18+18 = 14+18
x = 32

For the second equation, we solve for x by adding 18 to both sides:

x−18+18 = -14+18
x = 4

Therefore, the solutions to the quadratic equation are {32, 4}.