What number should be added to both sides of the equation to complete the square? x² – 6x= 5

Mathematics

1 answer:

astraxan [27]2 years ago

9 0

Answer:

x = 8.7 or x = 1.3

Step-by-step explanation:

x² – 6x= 5

(b/2)² = (6/2)² = 9 (Using Completing the square method)

x² – 6x + 9 = 5 + 9

(x -5)² = 14

x-5 = √14

x-5 = ±3.7

Either x-5 =3.7 or x-5 = -3.7

x = 3.7+5 or x = -3.7+5

x = 8.7 or x = 1.3

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Check the picture below.

$\bf \left. \qquad \right.\textit{internal division of a line segment}
\\\\\\
a(-1,2)\qquad b(7,14)\qquad
\qquad 1:3
\\\\\\
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\\\\
-------------------------------\\\\
{ P=\left(\cfrac{\textit{sum of "x" values}}{r1+r2}\quad ,\quad \cfrac{\textit{sum of "y" values}}{r1+r2}\right)}$

$\bf -------------------------------\\\\
P=\left(\cfrac{(3\cdot -1)+(1\cdot 7)}{1+3}\quad ,\quad \cfrac{(3\cdot 2)+(1\cdot 14)}{1+3}\right)
\\\\\\
P=\left( \cfrac{-3+7}{4}~,~\cfrac{6+14}{4} \right)$