How do you solve using the completing the square method $x^2+x=7/4$ ?

Question

1497 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-19T05:51:42

$x=0.91421356 or x=-1.91421356$

$color(red)(Commenci ng)$ $color(red)(compl e ti ng)$ $color(red)(the)$ $color(red)(squ are)$ $color(red)(method)$ $color(red)(now,)$

1) Know the formula for the perfect quadratic square, which is,

$(ax+-b)^2 = ax^2+-2abx+b^2$

2) Figure out your $a and b$ values,

$a=$ coefficient of $x^2$ , which is $1$ .
$color(red)(b=(1)/(2(1)) = 1/2)$

3) Add $color(red)(b^2)$ on both sides of the equation, giving you an overall net of 0, hence not affecting the result of the equation,

$x^2+x+color(red)((1/2)^2)=7/4+color(red)((1/2)^2)$
$(x+1/2)^2=2$

4) Square root both sides,

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

5) Subtract $1/2$ on both sides,

$x=+-sqrt2-1/2$

6) Calculate the two values of $x$ ,

$x=0.91421356 or x=-1.91421356$

How do you solve using the completing the square method x^2+x=7/4x^2+x=7/4?