How do you solve using the completing the square method $x^2 - 1/2 x - 3/16 = 0$ ?

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Answer 1 · 2016-09-19T08:50:23

$x = 3/4 " or " x= -1/4$

This involves adding the correct value to a quadratic expression to create a perfect square.

Recall: $(x-5)^2 = x^2 color(tomato)(-10)xcolor(tomato)(+25)" "larr color(tomato)(((-10)/2)^2 = +25)$

This relationship between $color(tomato)(b and c)$ will always exist.

If the value of $c$ is not the correct one, add on what you need.
However, if you have an equation add to BOTH sides.

$x^2 - 1/2 x - 3/16 = 0" " larr$ check: is $((-1)/2 div 2)^2 = -3/16?$ No

(the last term MUST be positive, because it is squared)

$x^2 - 1/2 x color(blue)(- 3/16) = 0" "larr$ not what we want, move it to RHS

$x^2 color(magenta)(- 1/2) x " +? " = color(blue)(3/16) "larr$ add on what you DO want

$[color(magenta)(-1/2) rarr div 2 rarr-1/4 rarr "squared" =color(red)(+1/16)]$

$x^2 - 1/2 x color(red)(+1/16) = 3/16 color(red)(+1/16) "larr$ add to BOTH sides

Now write the square of the binomial as $(x +?)^2$

$(xcolor(magenta)(-1/4))^2 = 4/16 = 1/4" "larrcolor(magenta)(-1/2 div 2 = -1/4)$

Now solve the equation - isolate $x$

$(x-1/4)^2 = 1/4$

$x-1/4 = +-sqrt(1/4)" "larr$ square root both sides

$x = +sqrt(1/4) +1/4 = 1/2+1/4 = 3/4$

Or

$x = -sqrt(1/4) +1/4 = -1/2 +1/4 = -1/4$

How do you solve using the completing the square method x^2 - 1/2 x - 3/16 = 0x^2 - 1/2 x - 3/16 = 0?