Which of the following is the solution to the following equation? 3x3/2+25=400

Question

(1 point)
Responses

125
125

5
5

25
25

250
250

Answer 1

To solve the equation \( 3x^{3/2} + 25 = 400 \), first, we can isolate the term with \( x \):

1. Subtract 25 from both sides: \[ 3x^{3/2} = 400 - 25 \] \[ 3x^{3/2} = 375 \]

2. Divide both sides by 3: \[ x^{3/2} = \frac{375}{3} \] \[ x^{3/2} = 125 \]

3. To solve for \( x \), raise both sides to the power of \( \frac{2}{3} \): \[ x = 125^{2/3} \]

4. We can calculate \( 125^{2/3} \):

   • Since \( 125 = 5^3 \), we have: \[ 125^{2/3} = (5^3)^{2/3} = 5^{3 \cdot \frac{2}{3}} = 5^2 = 25 \]

Thus, the solution to the equation \( 3x^{3/2} + 25 = 400 \) is \( x = 25 \).

Therefore, the correct response is: 25