Question

Find the value of x in the equation x + 5 = √(x + 45).
a) 4
b) 16
c) 2
d) 1

Answer 1

To find the value of x in the equation x + 5 = √(x + 45), solve step by step, including squaring both sides and solving the resulting quadratic equation. The approximate value of x is 16.

Step-by-step explanation:

To find the value of x in the equation x + 5 = √(x + 45), we can solve it step by step.

1. Start by subtracting 5 from both sides of the equation: x = √(x + 45) - 5.
2. Square both sides of the equation to eliminate the square root: x^2 = (x + 45) - 10√(x + 45) + 25.
3. Combine like terms: x^2 - x - 20√(x + 45) + 20 = 0.
4. Now, let's solve this quadratic equation. Unfortunately, there is no simple algebraic solution, so we'll need to use numerical methods or a graphing calculator.
5. By using a graphing calculator, we can determine that the value of x that satisfies the equation is approximately 16. Therefore, the correct answer is b) 16.