Is it possible to factor $y = \frac{x^{2}}{2} + 10 x + 22$ $y=x^2/2 +10x + 22$ ? If so, what are the factors?

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Is it possible to factor $y = \frac{x^{2}}{2} + 10 x + 22$ $y=x^2/2 +10x + 22$ ? If so, what are the factors?

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Answer 1 · 2016-02-09T21:05:12

This can not be factored using integer values.

$x ≅ - 2.57 or x ≅ 17.483 to 3 decimal places$ $" "x~= -2.57" or "x~=17.483" to 3 decimal places"$

Explanation:

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

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

That did not work so back to the formula

Standard form $\to a x^{2} + b x + c = 0$ $" "-> ax^2+bx+c=0$

where $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $" "x=(-b+-sqrt(b^2-4ac))/(2a)$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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

$x = \frac{- 10 \pm \sqrt{100 - 44}}{1}$ $x=(-10+-sqrt(100-44))/(1)$

$x = - 10 \pm \sqrt{56}$ $x=-10+-sqrt(56)$

$56 = 8 \times 7 \to \sqrt{56} = 2 \sqrt{14}$ $56=8xx7->sqrt(56)=2sqrt(14)$

So the factors are:

$[x - (10 + 2 \sqrt{14} .) .] [x - (10 - 2 \sqrt{14} .) .]$ $[x-(10+2sqrt(14)color(white)(.))color(white)(.)] [x-(10-2sqrt(14)color(white)(.) )color(white)(.)]$

$x ≅ - 2.57 or x ≅ 17.483$ $x~= -2.57" or "x~=17.483" "$ to 3 decimal places

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Is it possible to factor $y = \frac{x^{2}}{2} + 10 x + 22$ $y=x^2/2 +10x + 22$ ? If so, what are the factors?

1 Answer

Explanation:

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Is it possible to factor $y = \frac{x^{2}}{2} + 10 x + 22$ $y=x^2/2 +10x + 22$ ? If so, what are the factors?