Question

WILL GIVE BRAINLIEST

Answer 1

Part one:

$x^2-8x=-26$

Rewrite in the form $(x+a)^{2} =b$

$\left(x-4\right)^2=-10$

$\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

Solve $x-4=\sqrt{-10} : x=\sqrt{10} i+4$

Solve $x-4=\sqrt{-10} : x=-\sqrt{10} i+4$

$x=\sqrt{10}i+4,\:x=-\sqrt{10}i+4$

Part two:

$x=\frac{-\left(-8\right)\pm \sqrt{\left(-8\right)^2-4\cdot \:1\cdot \:26}}{2\cdot \:1}$

Simplify $\sqrt{\left(-8\right)^2-4\cdot \:1\cdot \:26}}: 2\sqrt{10} i$

$=\frac{-\left(-8\right)\pm \:2\sqrt{10}i}{2\cdot \:1}$

Separate solutions

$x_1=\frac{-\left(-8\right)+2\sqrt{10}i}{2\cdot \:1},\:x_2=\frac{-\left(-8\right)-2\sqrt{10}i}{2\cdot \:1}$

$\frac{-(-8)+2\sqrt{10}i }{2*1} :4+\sqrt{10}i$

$\frac{-(-8)+2\sqrt{10}i }{2*1} :4-\sqrt{10}i$

$x=4+\sqrt{10}i,\:x=4-\sqrt{10}i$