Answer:
To solve for x, we can start by cross-multiplying the equation:
sqrt(3.75) * (0.8 - x) = (0.8 + x)
Next, we can square both sides of the equation to eliminate the square root:
3.75 * (0.8 - x)^2 = (0.8 + x)^2
Expanding the square on the right side, we get:
3.75 * (0.64 - 1.6x + x^2) = 0.64 + 1.6x + x^2
Multiplying out the left side, we get:
2.4 - 6x + 3.75x^2 = 0.64 + 1.6x + x^2
Moving all the terms to one side, we get a quadratic equation:
3.75x^2 - 7.6x + 1.76 = 0
We can solve for x using the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 3.75, b = -7.6, and c = 1.76.
Plugging in the values, we get:
x = (-(-7.6) ± sqrt((-7.6)^2 - 4(3.75)(1.76))) / 2(3.75)
Simplifying, we get:
x = (7.6 ± sqrt(57.76 - 26.4)) / 7.5
x = (7.6 ± sqrt(31.36)) / 7.5
x = (7.6 ± 5.6) / 7.5
x = 1.2 / 7.5 or x = 13.2 / 7.5
x = 0.16 or x = 1.76
However, we need to check our solution because we squared both sides of the equation, which could introduce extraneous solutions. We can see that x = 1.76 does not satisfy the original equation, so it is an extraneous solution. Therefore, the only solution is x = 0.16.