How do you solve the quadratic equation by completing the square: $x^{2} - 6 x = 16$ $x^2 - 6x = 16$ ?

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Answer 1 · 2018-03-22T11:17:50

Solution: $x = 8 or x = - 2$ $x=8 or x=-2$

$x^{2} - 6 x = 16 or x^{2} - 6 x + 9 = 16 + 9$ $x^2-6x=16 or x^2-6x +9=16+9$

$:.(x-3)^2=25 or (x-3)=+-5$

$:.x= 3+5 or x=3-5$ or

$:.x=8 or x=-2$

Solution: $x=8 or x=-2$ [Ans]

Answer 2 · 2018-03-22T11:25:11

$x=8 or x=-2$

We have ,

$x^2-6x=16$

i.e. $x^2-6x+(-)=16+(-)$

To find third term, we use

$color(red)(3^(rd) term=(2^(nd) term)^2/(4xx1^(st)term)) =(-6x)^2/(4xxx^2)=(36x^2)/(4x^2)=9$

Adding both sides 9, we get

$x^2-6x+9=16+9=25$

$=>(x-3)^2=(5)^2$

Taking squareroot of both sides,

$=>x-3=+-5$

$:.x-3=5 or x-3=-5$

$:.x=8 or x=-2$

How do you solve the quadratic equation by completing the square: x^2 - 6x = 16x2−6x=16x^2 - 6x = 16?