Mathematics: WILL GIVE BRAINLIEST Hannah and Han are each trying to solve the equation x² – 8x + 26 = 0. They know that x = -1 are i& - i, but they are not sure how to use this information to solve for x in their equation. Part 1- Here is Hannah s work: x? - 8x + 26 = 0 X? – 8x = -26 Show Hannah how to finish her work using completing the square and complex numbers. Part 2- Han decides to solve the equation using the quadratic formula. Here is the beginning of his work -b+V62-4ac -(-8)+7-8)2–401|(26) Finish

1. None Of These2. Skew3. Perpendicular...

WILL GIVE BRAINLIEST Hannah and Han are each trying

genesisprieto11

24.07.2021

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

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

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

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

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

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