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}

Answer 1

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}.

Answer 2

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= .

Answer 3

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.