i think my main problem is that i don't understand the question but my friend tried explaining it and i didn't really get it ( i think its 2)
What is the absolute value of the product of the solutions of the equation below?
(x+2)^2=16
the solutions :
x+2 = +/- 4
so x = 2 or -6
the product of those solutions is -12
and the absolute value of that product would then be 12
thanks
To find the absolute value of the product of the solutions of the equation (x+2)^2 = 16, we need to first solve the equation and find the values of x.
Let's go step by step to solve the equation:
Step 1: Expand the equation
(x+2)^2 = 16
(x+2)(x+2) = 16
Step 2: Simplify the equation by using FOIL (First, Outer, Inner, Last)
x^2 + 4x + 4 = 16
Step 3: Move all the terms to one side to set the equation equal to zero
x^2 + 4x + 4 - 16 = 0
x^2 + 4x - 12 = 0
Step 4: Factor the equation or use the quadratic formula to find the values of x. In this case, it is easier to factor the quadratic equation:
(x+6)(x-2) = 0
Step 5: Set each factor equal to zero and solve for x:
x+6 = 0 or x-2 = 0
x = -6 or x = 2
Now, we have found the solutions of the equation as x = -6 and x = 2.
To find the absolute value of their product, we multiply these solutions:
|x| = |(-6)(2)| = 12
Therefore, the absolute value of the product of the solutions of the equation (x+2)^2 = 16 is 12.