Question

Complete the square to solve the equation below

x^2+x=7/4

A. x=-2+√2 ; x=-2 - √2
B. x=-1/2+√2 ; x=-1/2- √2
C. x=3 ; x=-1
D. x=1+√2 ; x=1- √2

Answer 1

$x^2+x= \frac{7}{4}$

Take one-half of the coefficient of x and square it, then add it to both sides.

$x^2+x+ (\frac{1}{4}) =\frac{7}{4}+ (\frac{1}{4})$

$x^2+x+(\frac{1}{4})= 2$

$\left(x+\frac{1}{2}\right)^2=2$

$x+\frac{1}{2}=\pm \sqrt{2}$
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$x+\frac{1}{2}=- \sqrt{2}$
$x=-\frac{1}{2}- \sqrt{2}$ <=

AND

$x+\frac{1}{2}= \sqrt{2}$
$x= \sqrt{2}-\frac{1}{2}$ <=