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Solve the equation using square roots.

2^2 - 26x + 169 = -13

Solve The Equation Using Square Roots 22 26x 169 13 class=

Sagot :

Eddie1Wanidn

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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