Quadratic equation can be written in the form...

Question

$y = 2x^2 + 5x - 3$ can be written in the form $y = 2(x+a)^2 + b$ . Find the value of $a$ and the value of $b$.

Edit: Answers were $a= 1.25, b= -6.125$.
I dont understand how that's the answer.

Answer 1

Expand \begin{align} (x+a)^2 &= x^2+2ax + a^2\\ \implies 2(x+a)^2 +b &= 2x^2+4ax+2a^2+b \end{align} Which allows for \begin{align} 4a&= 5\\ 2a^2 +b &= -3 \end{align} Now solve for $(a, b)$.

Answer 2

$$2x^2+5x-3=2\left(x^2+2x\cdot\frac{5}{4}+\frac{25}{16}-\frac{3}{2}-\frac{25}{16}\right)=$$ $$=2\left(x+\frac{5}{4}\right)^2-\frac{49}{8}.$$