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

Mar 19, 2017

$x = 0.91421356 \mathmr{and} x = - 1.91421356$

#### Explanation:

$\textcolor{red}{C o m m e n c i n g}$ $\textcolor{red}{c o m p l e t i n g}$ $\textcolor{red}{t h e}$ $\textcolor{red}{s q u a r e}$ $\textcolor{red}{m e t h o d}$ $\textcolor{red}{n o w ,}$

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

${\left(a x \pm b\right)}^{2} = a {x}^{2} \pm 2 a b x + {b}^{2}$

2) Figure out your $a \mathmr{and} b$ values,

$a =$ coefficient of ${x}^{2}$, which is $1$.
$\textcolor{red}{b = \frac{1}{2 \left(1\right)} = \frac{1}{2}}$

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

${x}^{2} + x + \textcolor{red}{{\left(\frac{1}{2}\right)}^{2}} = \frac{7}{4} + \textcolor{red}{{\left(\frac{1}{2}\right)}^{2}}$
${\left(x + \frac{1}{2}\right)}^{2} = 2$

4) Square root both sides,

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

5) Subtract $\frac{1}{2}$ on both sides,

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

6) Calculate the two values of $x$,

$x = 0.91421356 \mathmr{and} x = - 1.91421356$