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

Question

Responses

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

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

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

{253,−325}

Answer 1

To solve the equation $(x+36{)}^2-38=251$, we can follow these steps:

1. Isolate the squared term:

   $$(x+36{)}^2-38=251$$ $$(x+36{)}^2=251+38$$ $$(x+36{)}^2=289$$

2. Take square roots of both sides:

   $$x+36=\pm \sqrt{289}$$ $$x+36=\pm 17$$

3. Solve for $x$:

   • For the positive case: $$x+36=17$$ $$x=17-36$$ $$x=-19$$

   • For the negative case: $$x+36=-17$$ $$x=-17-36$$ $$x=-53$$

So, the solutions to the equation are:

$$-19,-53$$

Thus, the correct response is:

$-19,-53$