Question

What positive value of x makes the equation true? x ^ 2 + 2 x = 2 ( x+8 ).

A) √8
B) √4
C) 8
D) 4

Answer 1

To find the positive value of x for the equation x^2 + 2x = 2(x + 8), we simplify and solve for x. After simplifying, we get x^2 = 16, and taking the square root of both sides, we find that x = 4, which is the solution.

Step-by-step explanation:

The student is asking for the positive value of x that makes the equation x^2 + 2x = 2(x + 8) true. To solve for x, we first expand the right side of the equation and then subtract all terms to one side to set the equation to zero:

x^2 + 2x = 2x + 16

We then cancel out the 2x on both sides:

x^2 = 16

Now we take the square root of both sides:

x = ±√16

Since we are looking for the positive value of x:

x = 4

Hence, the positive value of x that satisfies the equation is 4, which corresponds to option D.