Question

( x - 9 ) ( x + 3 ) = -36 In the equation above , what is the value of x + 3? A. -6 B. 6 C. -4 D. 12

Answer 1

B: 6

Explanation:

To find the value of x + 3, we need to solve the given equation: (x - 9)(x + 3) = -36.

Expanding the equation, we get:

x^2 - 6x - 27 = -36

Rearranging the equation and simplifying, we have:

x^2 - 6x - 27 + 36 = 0

x^2 - 6x + 9 = 0

This is a quadratic equation. We can solve it by factoring or using the quadratic formula. In this case, the equation can be factored as:

(x - 3)(x - 3) = 0

Setting each factor equal to zero, we get:

x - 3 = 0

Solving for x, we find:

x = 3

Now, to find the value of x + 3:

x + 3 = 3 + 3 = 6

Therefore, the value of x + 3 is 6. So the answer is B.

Answer 2

To find the value of x + 3 in the given equation, we can solve it using the distributive property and then isolate the variable.

Expanding the equation, we have:

(x - 9)(x + 3) = -36

Using the distributive property, we can multiply each term:

x(x) + x(3) - 9(x) - 9(3) = -36

Simplifying further:

x^2 + 3x - 9x - 27 = -36

Combining like terms:

x^2 - 6x - 27 = -36

Moving all terms to one side to set the equation to zero:

x^2 - 6x - 27 + 36 = 0

x^2 - 6x + 9 = 0

Now we have a quadratic equation. We can solve it by factoring or using the quadratic formula. In this case, the equation can be factored as a perfect square:

(x - 3)^2 = 0

Taking the square root of both sides:

x - 3 = 0

Adding 3 to both sides:

x = 3

Finally, to find the value of x + 3:

x + 3 = 3 + 3 = 6

Therefore, the value of x + 3 is 6, so the correct answer is B. 6.