Can someone please solve this? ?

25^[x² + (3/2).x] = 125 → you know that: 25 = 5^(2)

[5^(2)]^[x² + (3/2).x] = 125 → you know that: 125 = 5^(3)

[5^(2)]^[x² + (3/2).x] = 5^(3) → recall: [x^(a)]^(b) = x^(ab)

5^{2.[x² + (3/2).x]} = 5^(3)

2.[x² + (3/2).x] = 3

x² + (3/2).x = 3/2

x² + (3/2).x + (3/4)² = (3/2) + (3/4)²

x² + (3/2).x + (3/4)² = 33/16

[x + (3/4)]² = 33/16

x + (3/4) = ± (√33)/4

x = - (3/4) ± [(√33)/4]

x = (- 3 ± √33)/4


Solution = { (- 3 - √33)/4 ; (- 3 + √33)/4 }

The answer is as follows:

Case 1:
25^(x^2)+3x/2=125
=>
x=-1.226597 with error E=0.0003<0.0005
using computer.

Case 2
25^(x^2+3x/2)=125
=>
5^(2x^2+3x)=5^3
=>
2x^2+3x=3
=>
x=[-3+/-sqr(9+24)]/4
=>
x=0.686140661 or x=-2.18614066.

25 x^2 + 3/2 x = 125
Multiply both sides by 2
50 x^2 + 3 x = 250
x (50 x + 3) = 250
Solutions:
x = -3/100 - sqrt(50009)/100
x = sqrt(50009)/100 - 3/100

What are you confused about? Every equation solver I've tried handles this well.

25x^2 + 3/2 x = 125
50x^2 + 3x - 250 = 0
Solutions:
x ≈ -2.2663
x ≈ 2.2663

The set is below