Questions: Solve 4+10 sqrt(x+8)=34 for x

Transcript text: Solve $4+10 \sqrt{x+8}=34$ for $x$

Solution

Solution Steps

To solve the equation $4 + 10 \sqrt{x+8} = 34$, we first isolate the square root term by subtracting 4 from both sides. Then, divide by 10 to solve for the square root. Finally, square both sides to eliminate the square root and solve for $x$.

Step 1: Isolate the Square Root Term

Start with the equation: \[ 4 + 10 \sqrt{x+8} = 34 \]

Subtract 4 from both sides to isolate the square root term: \[ 10 \sqrt{x+8} = 30 \]

Step 2: Solve for the Square Root

Divide both sides by 10 to solve for the square root: \[ \sqrt{x+8} = 3 \]

Step 3: Eliminate the Square Root

Square both sides to eliminate the square root: \[ x+8 = 9 \]

Step 4: Solve for $x$

Subtract 8 from both sides to solve for $x$: \[ x = 1 \]

Final Answer

$\boxed{x = 1}$

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