Answer:
x = 8
Explanation:
To solve the equation x(x - 2) = 48 for x, we can first expand the left side:
x^2 - 2x = 48
Next, we'll add 2x to both sides to isolate x^2:
x^2 = 48 + 2x
Then, we'll subtract 2x from both sides:
x^2 - 2x = 48
Now we have a quadratic equation that we can solve for x using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
where a = 1, b = -2, and c = 48. Plugging these values into the formula:
x = (-(-2) ± √((-2)^2 - 4(1)(48))) / 2(1)
x = (2 ± √(4 + 192)) / 2
x = (2 ± √196) / 2
x = (2 ± 14) / 2
So the two solutions are x = (2 + 14) / 2 = 8 and x = (2 - 14) / 2 = -6.
Keep in mind that x cannot be negative in this context as it represents a measurement. Therefore, x = 8 is the only solution that has a meaningful value in this context.