How have I dropped a factor 2 on the square root of 19?

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SUMMARY

The discussion centers on a mathematical problem involving the equation $15 = \frac{\left((x+3)+(2x-3)\right)h}{2}$, leading to the expression $30 = 3x^2 - 18x$. The user attempts to solve for x using the method of completing the square, resulting in $x^2 - 6x + 9 = 19$. A key point of confusion arises regarding the perceived omission of a factor of two in the square root of 19, which is clarified by other participants who confirm that no factor was actually missed.

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mathlearn
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The main problem is http://mathhelpboards.com/pre-algebra-algebra-2/find-length-dc-19355.html#post88492

In this question

$15 = \dfrac{\left((x+3)+(2x-3)\right)h}{2}=\frac12 ((x+3)+(2x-3))\times((2x-3) -(x+3))=\frac12((2x-3)^2-(x+3)^2)=\frac12(3 x^2-18 x)$

So we get $30=3x^2-18x$

Now using the complete the square method

$x^2-6x=10$
$x^2-6x+9=19$
$x=3\pm\sqrt {19}$

This is what I get , I know that i Have missed a factor of two on the square root of 19, How and why was that dropped?

:)
 
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mathlearn said:
I know that i Have missed a factor of two on the square root of 19
You have not.
 

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