How do you solve $4x^2+5=10x$ by completing the square?

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Answer 1 · 2017-06-04T16:08:50

$x = 1.809 or x = 0.691$

Re-arrange the equation to be equal to $0$ .

$4x^2 -10x+5=0" "larr$ make $1x^2rarr div 4$

$x^2 -5/2x color(red)(+5/4)=0$

$x^2 -5/2x color(white)(........)=color(red)(-5/4)$

$x^2 -5/2x color(blue)(+25/16)= -5/4color(blue)(+25/16)" "larr$ Add $color(blue)((b/2)^2)$ to both sides#

$(x-5/4)^2 color(white)(....)= 5/16$

$x- 5/4 = +-sqrt(5/16)$

$x = +sqrt(5/16)+5/4 = 1.809$

$x = -sqrt(5/16) +5/4 = 0.691$

How do you solve 4x^2+5=10x4x^2+5=10x by completing the square?