Question

Solve for x, given the equation Square root of x plus 9 − 4 = 1.

x = 16, solution is not extraneous

x = 16, solution is extraneous

x = 34, solution is not extraneous

x = 34, solution is extraneous

Answer 1

To solve the equation, isolate the square root term and square both sides to eliminate the square root. The solution to the equation is x = 16.

Step-by-step explanation:

To solve for x, we need to isolate the square root term on one side of the equation. Here are the steps to solve the equation:

1. Isolate the square root term. Subtract 9 from both sides of the equation to get: Square root of x - 4 = 1 - 9
2. Combine like terms. Simplify the right side of the equation to get: Square root of x - 4 = -8
3. Add 4 to both sides. This will isolate the square root term: Square root of x = -8 + 4
4. Combine like terms. Simplify the right side of the equation to get: Square root of x = -4
5. Square both sides. This will eliminate the square root: x = (-4)^2
6. Calculate the squared value. Evaluate (-4)^2 to get: x = 16

Therefore, the solution to the equation is x = 16.

Answer 2

The given condition may be mathematically expressed as,
sqrt (x) + 9 - 4 = 1
Group all the constants to the same side of the equation,
sqrt (x) = -4
Squaring both sides give an answer of x = 16.
The answer for the question above is x = 16 is not an extraneous root because if we substitute this value to the x of the equation, the equation becomes true.