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1524+2890-40sqrt? = 2/5 of 6410....

`1524+2890-40sqrt? = 2/5` of 6410.

A

2323

B

2026

C

2213

D

2116

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AI Generated Solution

The correct Answer is:
To solve the equation \( 1524 + 2890 - 40\sqrt{x} = \frac{2}{5} \times 6410 \), we will follow these steps: ### Step 1: Calculate the right side of the equation First, we need to calculate \( \frac{2}{5} \times 6410 \). \[ \frac{2}{5} \times 6410 = \frac{2 \times 6410}{5} = \frac{12820}{5} = 2564 \] ### Step 2: Combine the left side of the equation Next, we will combine \( 1524 + 2890 \). \[ 1524 + 2890 = 4414 \] ### Step 3: Set up the equation Now, we can set up the equation: \[ 4414 - 40\sqrt{x} = 2564 \] ### Step 4: Isolate the square root term Next, we will isolate \( 40\sqrt{x} \) by subtracting 2564 from both sides: \[ 4414 - 2564 = 40\sqrt{x} \] Calculating the left side: \[ 4414 - 2564 = 1850 \] So we have: \[ 40\sqrt{x} = 1850 \] ### Step 5: Solve for \( \sqrt{x} \) Now, divide both sides by 40: \[ \sqrt{x} = \frac{1850}{40} \] Calculating the right side: \[ \sqrt{x} = 46.25 \] ### Step 6: Square both sides to find \( x \) Now, square both sides to solve for \( x \): \[ x = (46.25)^2 \] Calculating \( (46.25)^2 \): \[ x = 2146.5625 \] ### Step 7: Final answer Thus, the value of \( x \) is approximately: \[ x \approx 2146.56 \]
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