Solve the following quadratic equation using square roots: (x+36)^2−38=251 .(1 point) Responses {253,−325} left brace 253 comma negative 325 right brace {−19,−53} left brace negative 19 comma negative 53 right brace {53,19} left brace 53 comma 19 right brace {17.84,−13.84}
To solve the equation using square roots, we can first isolate the squared term:
(x+36)^2 - 38 = 251
(x+36)^2 = 289
Next, we can take the square root of both sides:
√((x+36)^2) = ±√289
x + 36 = ±17
Now, we can solve for x by subtracting 36 from both sides:
x = -36 ± 17
This gives two possible solutions:
x = -36 + 17 = -19
x = -36 - 17 = -53
Therefore, the solutions to the quadratic equation are:
{ -19, -53 }