How do you solve using the completing the square method 2x^2 - x - 5 = 02x2−x−5=0?

1 Answer
Tony B
Mar 10, 2016

" "2(x-1/4)^2-41/8 => "vertex" -> (x,y) -> (1/4,-41/8) 2(x−14)2−418⇒vertex→(x,y)→(14,−418)

x-axis and y-axis Intercepts can be found in the normal way

Explanation:

For a more in depth approach have a look at my solution to
http://socratic.org/s/asD9k2Ch. Diferent values but the method is sound.

Write as:" "2(x^2-color(red)(1/2)x)-5=0 2(x2−12x)−5=0

For the color(red)(-1/2)" in "-1/2x−12 in −12x apply: (-1/2)xx(color(red)(-1/2)) = + 1/4(−12)×(−12)=+14

So the left hand side becomes:

" "2(x^2-1/4color(green)(x))-5 2(x2−14x)−5

Remove the color(green)(x)x

" "2(x^(color(magenta)(2))-1/4)-5 2(x2−14)−5

Move the index (power) color(magenta)(2)2 to outside the brackets

" "2(xcolor(red)(-1/4))^(color(magenta)(2)) -5 2(x−14)2−5

Square the constant color(red)((-1/4)^2=+1/16(−14)2=+116 and subtract twice its value color(red)(2xx(=1/4)^2=+1/8)2×(=14)2=+18

" "2(x-1/4)^2-5-1/8 2(x−14)2−5−18

" "2(x-1/4)^2-41/8 2(x−14)2−418

'~~~~~~~~~~~~~~~~~~~~~~~~~~~
x_("vertex") = (-1)xx(-1/4)= +1/4xvertex=(−1)×(−14)=+14

y_("vertex")= -41/8 =-5 1/8yvertex=−418=−518

Tony B

Related questions
See all questions in Completing the Square
Impact of this question
1639 views around the world
You can reuse this answer
Creative Commons License