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

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

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Answer 1 · 2017-03-19T05:51:42

$x = 0.91421356 or x = - 1.91421356$ $x=0.91421356 or x=-1.91421356$

Explanation:

$C o m m e n c i n g$ $color(red)(Commenci ng)$ $c o m p l e t i n g$ $color(red)(compl e ti ng)$ $t h e$ $color(red)(the)$ $s q u a r e$ $color(red)(squ are)$ $m e t h o d$ $color(red)(method)$ $n o w,$ $color(red)(now,)$

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

${(a x \pm b)}^{2} = a x^{2} \pm 2 a b x + b^{2}$ $(ax+-b)^2 = ax^2+-2abx+b^2$

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

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

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

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

4) Square root both sides,

$x + \frac{1}{2} = \pm \sqrt{2}$ $x+1/2=+-sqrt(2)$

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

$x = \pm \sqrt{2} - \frac{1}{2}$ $x=+-sqrt2-1/2$

6) Calculate the two values of $x$ $x$ ,

$x = 0.91421356 or x = - 1.91421356$ $x=0.91421356 or x=-1.91421356$

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