We have the following:
[tex]2x^2+3x-1=0[/tex]Claim:
The x-intercepts for the quadratic equation are the solutions of the equation.
Evidence:
[tex]\begin{gathered} \frac{2}{2}x^2+\frac{3}{2}x-\frac{1}{2}=0 \\ x^2+\frac{3}{2}x+(\frac{3}{4})^2=\frac{1}{2}+(\frac{3}{4})^2 \\ (x+\frac{3}{4})^2=\frac{17}{16} \\ x+\frac{3}{4}=\pm\sqrt[]{\frac{17}{16}} \\ x=\pm\sqrt[]{\frac{17}{16}}-\frac{3}{4} \end{gathered}[/tex]Reasoning:
It was solved by obtaining a binomial squared
Which means that the intercepts are:
[tex]\begin{gathered} (\sqrt[]{\frac{17}{16}}-\frac{3}{4},0)\rightarrow(0.28,0) \\ (-\sqrt[]{\frac{17}{16}}-\frac{3}{4},0)\rightarrow(-1.78,0) \end{gathered}[/tex]