Solve the following quadratic equation using square roots: (x+36)2−38=251.(1 point)
Responses
{53,19}
left brace 53 comma 19 right brace
{17.84,−13.84}
left brace 17.84 comma negative 13.84 right brace
{253,−325}
left brace 253 comma negative 325 right brace
{−19,−53}
To solve the quadratic equation (x+36)^2 - 38 = 251 using square roots, we can follow these steps:
Step 1: Simplify the equation.
(x+36)^2 - 38 = 251
(x+36)^2 = 251 + 38
(x+36)^2 = 289
Step 2: Take the square root of both sides.
√(x+36)^2 = √289
x+36 = ±17
Step 3: Solve for x.
x = -36 + 17 or x = -36 - 17
Therefore, the solutions to the quadratic equation are x = -36 + 17 or x = -36 - 17, which simplifies to x = -19 or x = -53.
The correct answer is {−19,−53}.