# Is it possible to factor y=x^2/2 +10x + 22 ? If so, what are the factors?

Feb 9, 2016

This can not be factored using integer values.

$\text{ "x~= -2.57" or "x~=17.483" to 3 decimal places}$

#### Explanation:

given: $\text{ } y = \frac{1}{2} {x}^{2} + 10 x + 22$

$y = \frac{1}{2} \left({x}^{2} + 5 x + 11\right)$

That did not work so back to the formula

Standard form$\text{ } \to a {x}^{2} + b x + c = 0$

where$\text{ } x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
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x=(-10+-sqrt(10^2-4(1/2)(22)))/(2(1/2)

$x = \frac{- 10 \pm \sqrt{100 - 44}}{1}$

$x = - 10 \pm \sqrt{56}$

$56 = 8 \times 7 \to \sqrt{56} = 2 \sqrt{14}$

So the factors are:

$\left[x - \left(10 + 2 \sqrt{14} \textcolor{w h i t e}{.}\right) \textcolor{w h i t e}{.}\right] \left[x - \left(10 - 2 \sqrt{14} \textcolor{w h i t e}{.}\right) \textcolor{w h i t e}{.}\right]$

$x \cong - 2.57 \text{ or "x~=17.483" }$ to 3 decimal places