Question

Solve the equation using square roots. 2^2 - 26x + 169 = -13

Answer 1

$\\ \sf\longmapsto x^2-26x+169=-13$

$\\ \sf\longmapsto x^2-26x=-182$

$\\ \sf\longmapsto x^2-2(13)x=-182$

$\\ \sf\longmapsto x^2-2(13)x+13^2=13^2-182$

$\\ \sf\longmapsto (x-13)^2=-13$

$\\ \sf\longmapsto x-13=\pm\sqrt{13}i$

$\\ \sf\longmapsto x=13\pm \sqrt{13}i$

Answer 2

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