Solve the following quadratic equation using square roots: (x−18)^2=196 .(1 point)
Responses
{214,−178}
left brace 214 comma negative 178 right brace
{32,4}
left brace 32 comma 4 right brace
{21,5}
left brace 21 comma 5 right brace
{−4,−32}
To solve the quadratic equation (x-18)^2 = 196, we can start by taking the square root of both sides:
√((x-18)^2) = √196
Simplifying the left side, we have:
|x-18| = 14
Next, we can split the equation into two separate equations:
x-18 = 14 or x-18 = -14
Solving the first equation, we can add 18 to both sides:
x = 14 + 18
x = 32
Solving the second equation, we can add 18 to both sides:
x = -14 + 18
x = 4
Therefore, the solutions to the quadratic equation (x-18)^2 = 196 are {32, 4}.