Question

Solving quadratic function by completing the squares

Answer 1

Consider the given equation,

`-32=2(x^2+10)`

Apply the method of completing square as follows,

`\begin{gathered} -32=2(x^2+2(x)(5)) \\ -32+50=2(x^2+2(x)(5))+2(25) \\ 18=2(x^2+2(x)(5)+25) \\ 18=2(x^2+2(x)(5)+(5)^2) \\ 18=2(x+5)^2 \\ (18)/(2)=(x+5)^2 \\ (x+5)^2=9 \\ x+5=\sqrt[]{9} \\ x+5=\pm3 \\ x+5=3\text{ }or\text{ }x+5=-3 \\ x=3-5\text{ }or\text{ }x=-3-5 \\ x=-2\text{ }or\text{ }x=-8 \end{gathered}`

Thus, the solutions of the quadratic equation are -2 and -8.