Solve the following quadratic equation using square roots: (x+36)^2−38=251.
{253,−325} left brace 253 comma negative 325 right brace {53,19} left brace 53 comma 19 right brace {17.84,−13.84} left brace 17.84 comma negative 13.84 right brace {−19,−53}
To solve the equation (x+36)^2 - 38 = 251 using square roots, we can first isolate the square term on one side of the equation:
(x+36)^2 = 251 + 38
(x+36)^2 = 289
Next, we take the square root of both sides to eliminate the square on the left side:
(x+36) = ±√289
(x+36) = ±17
Now, we solve for x by removing the 36 from both sides:
x = -36 ± 17
Therefore, the solutions to the quadratic equation are:
x = -36 + 17 = -19
x = -36 - 17 = -53
The solutions are {-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^2 + 72x + 1296 - 38 = 251
x^2 + 72x + 1296 - 38 - 251 = 0
x^2 + 72x + 1007 = 0
Step 2: Move the constant term to the right side of the equation
x^2 + 72x = -1007
Step 3: Complete the square by adding (b/2)^2 to both sides, where b is the coefficient of x
The coefficient of x is 72, so (72/2)^2 = 1296
x^2 + 72x + 1296 = -1007 + 1296
(x + 36)^2 = 289
Step 4: Take the square root of both sides
x + 36 = ±√289
x + 36 = ±17
Step 5: Solve for x
x = -36 + 17
x = -19
or
x = -36 - 17
x = -53
Therefore, the solutions to the quadratic equation are x = -19 and x = -53, expressed as a set: {-19, -53}.
To solve the quadratic equation (x+36)^2−38=251 using square roots, we can follow these steps:
Step 1: Expand the expression.
(x+36)^2−38 = 251
(x+36)(x+36)−38 = 251
x^2 + 72x + 1296 −38 = 251
x^2 + 72x + 1258 = 251
Step 2: Move the constant term to the other side.
x^2 + 72x + 1258 - 251 = 0
x^2 + 72x + 1007 = 0
Step 3: Identify the coefficient values.
In this case, a = 1, b = 72, and c = 1007.
Step 4: Use the quadratic formula.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the values from our equation:
x = ( - 72 ± √(72^2 - 4 * 1 * 1007)) / (2 * 1)
Step 5: Simplify the equation and compute the solutions.
x = ( - 72 ± √(5184 - 4028)) / 2
x = ( - 72 ± √(1156)) / 2
x = ( - 72 ± 34) / 2
Therefore, the solutions to the equation are:
x1 = ( - 72 + 34) / 2 = -19
x2 = ( - 72 - 34) / 2 = -53
Hence, the correct answer is {−19,−53}.