Question

What are the roots of the equation id="TexFormula1" title=" {x}^{2} - 16x + 89 = 0" alt=" {x}^{2} - 16x + 89 = 0" align="absmiddle" class="latex-formula">
in simplest a+bi form?

Answer 1

By completing the square,

$x^2-16x+89=x^2-16x+64+25=(x-8)^2+25=0$

$(x-8)^2=-25$

$x-8=\pm\sqrt{-25}$

$x=8\pm5i$