What number should be added to the expression \(x^2 - 15x\) to result in an expression equivalent to a perfect square?

Noah uses the quadratic formula to solve the equation \(2x^2+3x-5=4\). He finds \(x = \text-2.5\) or 1. But, when he checks his answer, he finds that neither -2.5 nor 1 are solutions to the equation. Here are his steps:

\(a=2\), \(b=3\), \(c=\text-5\)

\(x=\frac{\text-3 \pm \sqrt{3^2 - 4 \boldcdot 2 \boldcdot \text-5}}{2 \boldcdot 2}\)

\(x=\frac{\text-3 \pm \sqrt{49}}{4}\)

\(x = \text-2.5\) or 1

1. Explain what Noah’s mistake was.
2. Solve the equation correctly.