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 {253,−325} left brace 253 comma negative 325 right brace {−19,−53} left brace negative 19 comma negative 53 right brace {17.84,−13.84}
To solve the quadratic equation (x+36)^2 - 38 = 251, we first need to simplify the equation:
(x+36)^2 - 38 = 251
(x+36)^2 = 289
Taking the square root of both sides:
x+36 = ±17
x = -36 ± 17
So the solutions are:
x = -36 + 17 = -19
x = -36 - 17 = -53
Therefore, the correct answer is { -19, -53 }.
To solve the quadratic equation (x+36)^2 - 38 = 251 using square roots, follow these steps:
Step 1: Expand the equation:
(x+36)^2 - 38 = 251
(x+36)(x+36) - 38 = 251
(x+36)(x+36) = 289
Step 2: Take the square root of both sides:
√[(x+36)(x+36)] = √289
(x+36) = ±√289
Step 3: Simplify the square root:
(x+36) = ±17
Step 4: Solve for x:
For the positive square root:
x + 36 = 17
x = 17 - 36
x = -19
For the negative square root:
x + 36 = -17
x = -17 - 36
x = -53
So, the solutions to the quadratic equation are:
x = -19 and x = -53
To solve the quadratic equation (x+36)² - 38 = 251 using square roots, we can follow these steps:
Step 1: Move the constant term to the other side of the equation:
(x+36)² - 38 + 38 = 251 + 38
(x+36)² = 289
Step 2: Take the square root of both sides:
√((x+36)²) = √289
Step 3: Simplify the square root and solve for x:
x + 36 = ±17
Step 4: Solve for x in each case:
Case 1: x + 36 = 17
Solving for x, we subtract 36 from both sides:
x = 17 - 36
x = -19
Case 2: x + 36 = -17
Solving for x, we subtract 36 from both sides:
x = -17 - 36
x = -53
Therefore, the solutions to the quadratic equation are {x = -19, x = -53}.