Solve the following quadratic equation using square roots: (x+36)2−38=251 .(1 point)

Question

Responses

{253,−325}
left brace 253 comma negative 325 right brace

{17.84,−13.84}
left brace 17.84 comma negative 13.84 right brace

{−19,−53}
left brace negative 19 comma negative 53 right brace

{53,19}

Answer 1

To solve the quadratic equation \((x + 36)^2 - 38 = 251\), we first isolate the squared term.

Starting from the equation: \[ (x + 36)^2 - 38 = 251 \]

Add 38 to both sides: \[ (x + 36)^2 = 251 + 38 \] \[ (x + 36)^2 = 289 \]

Now, we take the square root of both sides. Remember to include both the positive and negative roots: \[ x + 36 = \pm 17 \]

This gives us two equations to solve:

1. \(x + 36 = 17\)
2. \(x + 36 = -17\)

Solving the first equation: \[ x + 36 = 17 \] Subtract 36 from both sides: \[ x = 17 - 36 \] \[ x = -19 \]

Solving the second equation: \[ x + 36 = -17 \] Subtract 36 from both sides: \[ x = -17 - 36 \] \[ x = -53 \]

Thus, the solutions are: \[ x = -19 \quad \text{and} \quad x = -53 \]

The correct answer is: \[ {-19, -53} \]