You can't do that!

Algebra Level 1

8x+13+2x3=5\large \sqrt{8x + 13} + \sqrt{2x - 3} = 5 Jason came across the above problem in his algebra test and solved it as follows: 8x+13+2x3=5(8x+13+2x3)2=528x+13+2x3=2510x+10=25x=32.\begin{aligned} \sqrt{8x + 13} + \sqrt{2x - 3} & = 5 \\ \big(\sqrt{8x + 13} + \sqrt{2x - 3}\big)^2 & = 5^2 \\ 8x + 13 + 2x - 3 & = 25 \\ 10x + 10 & = 25 \\ \Rightarrow x & = \frac 32. \end{aligned} We can see that the cancellation of square roots in step 3 is fallacious. So, what's the correct answer (to 2 decimal places)?

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