Solve the following quadratic equation using square roots: (x+36)2−38=251 .(1 point) Responses {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 {253,−325} left brace 253 comma negative 325 right brace {53,19}

To solve the quadratic equation using square roots, we need to isolate the squared term on one side of the equation.

Starting with (x+36)² - 38 = 251, we can begin by adding 38 to both sides to move it to the other side:

(x+36)² = 289

Next, we can take the square root of both sides to eliminate the squared term:

x+36 = ±√289

√289 can be simplified to 17, so we have:

x+36 = ±17

To solve for x, we subtract 36 from both sides of the equation:

x = -36 ± 17

This gives us two possible solutions:

x = -36 + 17 = -19

x = -36 - 17 = -53

So the solutions to the quadratic equation are x = -19 and x = -53.

Therefore, the correct response is: {−19,−53}.

Use the Zero Product Property to find the value of x that makes the following statement true: 2⋅(x−3)=0 .(1 point) The value that makes the statement true is x= .

To use the Zero Product Property to find the value of x that makes 2⋅(x−3)=0 true, we set each factor equal to zero and solve for x.

The two factors in this equation are 2 and (x-3). So we have:

2 = 0 or x-3 = 0

Since the equation 2 = 0 is not true, we can ignore it.

To solve the equation x-3 = 0, we add 3 to both sides of the equation:

x - 3 + 3 = 0 + 3

This simplifies to:

x = 3

Therefore, the value that makes the statement true is x = 3.

To solve the quadratic equation (x+36)^2 - 38 = 251 using square roots, we can follow these steps:

Step 1: Expand the Equation
Expand the squared term (x+36)^2 to get: x^2 + 72x + 1296. The equation then becomes: x^2 + 72x + 1296 - 38 = 251.

Step 2: Simplify the Equation
Combine like terms to simplify the equation: x^2 + 72x + 1258 = 251.

Step 3: Move Constants to the Other Side
To isolate the squared term and x term, subtract 251 from both sides of the equation: x^2 + 72x + 1258 - 251 = 0. This results in: x^2 + 72x + 1007 = 0.

Step 4: Apply the Quadratic Formula
Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation (in the format ax^2 + bx + c = 0), we can find the solutions.

From the equation x^2 + 72x + 1007 = 0, we have:
a = 1 (coefficient of x^2),
b = 72 (coefficient of x),
c = 1007 (constant).

Plugging these values into the quadratic formula, we get:
x = (-72 ± √(72^2 - 4 * 1 * 1007)) / (2 * 1).

Simplifying the equation further:
x = (-72 ± √(5184 - 4028)) / 2.
x = (-72 ± √1156) / 2.
x = (-72 ± 34) / 2.

Step 5: Solve for x
Using the two different values of ±34, we can solve for x:

For the positive square root:
x = (-72 + 34) / 2 = -19.

For the negative square root:
x = (-72 - 34) / 2 = -53.

Therefore, the solutions to the quadratic equation (x+36)^2 - 38 = 251 using square roots are:
x = -19 and x = -53.