Answer:
x = 4 + √3 and x = 4 − √3
Step-by-step explanation:
(a−b)^2=a^2−2ab+b2
a^2−b^2=(a−b)(a+b)
−2x^2+16x−26
=−2(1x^2−8x+13)
=−2(x^2−8x+13+3−3)
=−2(x^2−8x+16−3)
=−2(x^2−2(4)x+4^2−3)
=−2((x−4)^2−3)
=−2((x−4)^2−(√3)^2)
=−2((x−4)−√3)((x−4)+√3)
=−2((x−(4+√3)((x−(4−√3))
The zeros of the given algebraic expression are:
−2x^2+16x−26=0
−2((x−(4+√3)((x−(4−√3))=0
x = 4 + √3 and x = 4 − √3
I strongly suggest using the quadratic formula as this problem is much easier to solve using it.
x = (−b ± [tex]\sqrt{b^{2}-4ac }[/tex] ) / 2
