If the equation $9\sqrt{x}−7\sqrt{x}−36$ = -16, then the value of 'x' is :

Q: If the equation $9\sqrt{x}−7\sqrt{x}−36$ = -16, then the value of 'x' is :

To solve the equation $9\sqrt{x} - 7\sqrt{x} - 36 = -16$, we need to find the value of $x$ that satisfies this equation. Let's go through the solution step by step: 1. **Simplify the Equation:** The given equation is: \[ 9\sqrt{x} - 7\sqrt{x} - 36 = -16 \] Combine like terms: \[ (9\sqrt{x} - 7\sqrt{x}) - 36 = -16 \] \[ 2\sqrt{x} - 36 = -16 \] 2. **Isolate the Square Root Term:** Add 36 to both sides of the equation to isolate the square root term: \[ 2\sqrt{x} = -16 + 36 \] \[ 2\sqrt{x} = 20 \] 3. **Solve for $\sqrt{x}$:** Divide both sides by 2: \[ \sqrt{x} = \frac{20}{2} \] \[ \sqrt{x} = 10 \] 4. **Solve for $x$:** Square both sides to solve for $x$: \[ x = 10^2 \] \[ x = 100 \] Thus, the value of $x$ is 100, which corresponds to Option 4. **Explanation for Incorrect Options:** - **Option 1 (5):** If $x = 5$, then $\sqrt{x} = \sqrt{5}$. Substituting into the equation: \[ 9\sqrt{5} - 7\sqrt{5} - 36 \neq -16 \] This does not satisfy the equation. - **Option 2 (10):** If $x = 10$, then $\sqrt{x} = \sqrt{10}$. Substituting into the equation: \[ 9\sqrt{10} - 7\sqrt{10} - 36 \neq -16 \] This does not satisfy the equation. - **Option 3 (20):** If $x = 20$, then $\sqrt{x} = \sqrt{20}$. Substituting into the equation: \[ 9\sqrt{20} - 7\sqrt{20} - 36 \neq -16 \] This does not satisfy the equation. Therefore, Option 4 is the only correct answer, as it satisfies the given equation.

Question

Accepted Answer

To solve the equation $9\sqrt{x} - 7\sqrt{x} - 36 = -16$, we need to find the value of $x$ that satisfies this equation. Let's go through the solution step by step:

1. **Simplify the Equation:**
   The given equation is:
   $$
   9\sqrt{x} - 7\sqrt{x} - 36 = -16
   $$
   Combine like terms:
   $$
   (9\sqrt{x} - 7\sqrt{x}) - 36 = -16
   $$
   $$
   2\sqrt{x} - 36 = -16
   $$

2. **Isolate the Square Root Term:**
   Add 36 to both sides of the equation to isolate the square root term:
   $$
   2\sqrt{x} = -16 + 36
   $$
   $$
   2\sqrt{x} = 20
   $$

3. **Solve for $\sqrt{x}$:**
   Divide both sides by 2:
   $$
   \sqrt{x} = \frac{20}{2}
   $$
   $$
   \sqrt{x} = 10
   $$

4. **Solve for $x$:**
   Square both sides to solve for $x$:
   $$
   x = 10^2
   $$
   $$
   x = 100
   $$

Thus, the value of $x$ is 100, which corresponds to Option 4.

**Explanation for Incorrect Options:**

- **Option 1 (5):** If $x = 5$, then $\sqrt{x} = \sqrt{5}$. Substituting into the equation:
  $$
  9\sqrt{5} - 7\sqrt{5} - 36 \neq -16
  $$
  This does not satisfy the equation.

- **Option 2 (10):** If $x = 10$, then $\sqrt{x} = \sqrt{10}$. Substituting into the equation:
  $$
  9\sqrt{10} - 7\sqrt{10} - 36 \neq -16
  $$
  This does not satisfy the equation.

- **Option 3 (20):** If $x = 20$, then $\sqrt{x} = \sqrt{20}$. Substituting into the equation:
  $$
  9\sqrt{20} - 7\sqrt{20} - 36 \neq -16
  $$
  This does not satisfy the equation.

Therefore, Option 4 is the only correct answer, as it satisfies the given equation.