How do you find all the real and complex roots of $x^2 + 10x + 26 = 0$ ?

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How do you find all the real and complex roots of $x^2 + 10x + 26 = 0$ ?

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Answer 1 · 2018-07-19T22:47:58

$x = -5+-i$

Explanation:

We can complete the square then use the difference of squares identity:

$A^2-B^2 = (A-B)(A+B)$

with $A=(x+5)$ and $B=i$ as follows:

$0 = x^2+10x+26$

$color(white)(0) = x^2+2(x)(5)+(5)^2+1$

$color(white)(0) = (x+5)^2-i^2$

$color(white)(0) = ((x+5)-i)((x+5)+i)$

$color(white)(0) = (x+5-i)(x+5+i)$

Hence:

$x = -5+-i$

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How do you find all the real and complex roots of $x^2 + 10x + 26 = 0$ ?

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How do you find all the real and complex roots of $x^2 + 10x + 26 = 0$ ?