To solve the quadratic equation using square roots, first make sure the equation is in the correct form:
\[(x+36)^2 - 38 = 251\]
Bring the constant term to the right side of the equation:
\[(x+36)^2 = 251 + 38\]
Solve the right side:
\[(x+36)^2 = 289\]
Now, take the square root of both sides:
\[x + 36 = \pm \sqrt{289}\]
Since \(289 = 17^2\), the square root of 289 is 17:
\[x + 36 = \pm 17\]
Now we have two possible solutions when we consider the positive and negative square roots:
\[x + 36 = 17\]
\[x = 17 - 36\]
\[x = -19\]
And
\[x + 36 = -17\]
\[x = -17 - 36\]
\[x = -53\]
So, the two solutions are:
\[\{ -19, -53 \}\]
Therefore, the correct response is:
\[{ -19, -53 }\]
left brace negative 19 comma negative 53 right brace
Solve the following quadratic equation using square roots: (x+36)2−38=251.(1 point)%0D%0AResponses%0D%0A%0D%0A{53,19}%0D%0Aleft brace 53 comma 19 right brace%0D%0A%0D%0A{17.84,−13.84}%0D%0Aleft brace 17.84 comma negative 13.84 right brace%0D%0A%0D%0A{−19,−53}%0D%0Aleft brace negative 19 comma negative 53 right brace%0D%0A%0D%0A{253,−325}%0D%0Aleft brace 253 comma negative 325 right brace
1 answer