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Sagot :
Answer:
x=13+√-13 or x=13-√-13
Step-by-step explanation:
Using the method of completing the square roots:
x²-26x=-13-169
x²-26x=-182
x²-26x+(-13)²=-182+(-13)²
(x-13)²=-182+169
(x-13)²=-13
Take square roots of both sides
(x-13)=√-13
x=13±√-13
That can also be written as
X=13+√13i,13-√13i
[tex]\\ \sf\longmapsto x^2-26x+169=-13[/tex]
[tex]\\ \sf\longmapsto x^2-26x=-182[/tex]
[tex]\\ \sf\longmapsto x^2-2(13)x=-182[/tex]
[tex]\\ \sf\longmapsto x^2-2(13)x+13^2=13^2-182[/tex]
[tex]\\ \sf\longmapsto (x-13)^2=-13[/tex]
[tex]\\ \sf\longmapsto x-13=\pm\sqrt{13}i[/tex]
[tex]\\ \sf\longmapsto x=13\pm \sqrt{13}i[/tex]
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