Final answer:
To find the value of x, rewrite the given equation as (1 + sqrt(x))^2 = 25. Expand and simplify to get x + 2sqrt(x) - 24 = 0. Use the substitution a = sqrt(x) to solve the quadratic equation a^2 + 2a - 24 = 0. Find the positive value of a, which is 4, and square it to find x = 16.
Step-by-step explanation:
To find the value of x, we can start by rewriting the given equation: (1 + √x)2 = 25. Expanding the square on the left side gives us 1 + 2√x + x = 25. Simplifying further, we have 2√x + x = 24. Combining like terms, we get x + 2√x - 24 = 0.
This equation is quadratic in form, so we can solve it by letting √x = a. Substituting, we get a2 + 2a - 24 = 0. Factoring or using the quadratic formula gives us (a + 6)(a - 4) = 0. Therefore, a = -6 or a = 4.
Since √x = a, we can ignore the negative value and conclude that √x = 4. Squaring both sides, we find that x = 16. Therefore, the value of x is 16.