If `d^(2)=sqrt(4)+d+10`, what is the value of d?

Options

A. `2`
B. `3`
C. `4`
D. `10`

Answer

To solve the equation \( d^2 = \sqrt{4} + d + 10 \), we will follow these steps:

### Step 1: Simplify the square root
First, we simplify the square root on the right side of the equation:
\[ \sqrt{4} = 2 \]
So we can rewrite the equation as:
\[ d^2 = 2 + d + 10 \]

### Step 2: Combine like terms
Next, we combine the constant terms on the right side:
\[ d^2 = d + 12 \]

### Step 3: Rearrange the equation
Now, we rearrange the equation to bring all terms to one side:
\[ d^2 - d - 12 = 0 \]

### Step 4: Factor the quadratic equation
We will factor the quadratic equation \( d^2 - d - 12 \). We need two numbers that multiply to \(-12\) and add to \(-1\). The numbers \(-4\) and \(3\) work:
\[ (d - 4)(d + 3) = 0 \]

### Step 5: Solve for \(d\)
Now, we set each factor equal to zero:
1. \(d - 4 = 0 \Rightarrow d = 4\)
2. \(d + 3 = 0 \Rightarrow d = -3\)

### Step 6: Identify valid solutions
Since we are looking for the value of \(d\) in the context given, we note that both \(4\) and \(-3\) are solutions to the equation. However, if we consider the context of the problem (as indicated in the video), we may only take the positive solution:
\[ d = 4 \]

### Final Answer
Thus, the value of \(d\) is:
\[ \boxed{4} \]

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