Question 348136

Hi,
If I am understanding your question properly:
{{{root(2,(x+4))+2 =root(2, (x+20))}}}
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SQUARE BOTH SIDES OF THE EQUATION:
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squaring left side gives:
{{{((root(2,(x+4)))+2)^2 = x+4 + 4*root(2,(x+4)) + 4 }}}
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squaring right gives (x+20)
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Result of squaring both sides of the equation:
{{{x+4 + 4*root(2,(x+4)) + 4 = (x + 20)}}}
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Simplifying
{{{root(2,(x+4))= 3}}}
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SQUARING BOTH SIDES OF THIS EQUATION
x+4 = 9
x=5
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this is solved as above: fist Squaring both sides of the equation, simplifying and once again squaring both sides of the equation to solve for x
{{{5*root(2,(x-2))-3 =root(2, (19*x+29))}}}
Square both sides to get:
{{{25(x-2) - 30sqrt(x-2) + 9 = 19x-29}}}
{{{25x-50 - 30sqrt(x-2) = 19x-38}}}
{{{-30sqrt(x-2) = 12-6x}}}
{{{(6x-12)= 30sqrt(x-2)}}}
{{{(x-2)= 5sqrt(x-2)}}}
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SQUARE BOTH SIDES
{{{x^2 -4x +4 = 25(x-2)}}}
{{{x^2 -4x +4 = 25x-50)}}}
{{{x^2 -29x +54= 0}}}
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factor
{{{(x-27)(x-2)=0}}}
x=27 or x=2