Question 155420
{{{ 12/sqrt(5x+6) = sqrt(2x+5) }}}
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To find 'x', start by multiplying both sides by {{{ sqrt(5x+6) }}}
{{{ (12/sqrt(5x+6))sqrt(5x+6) = sqrt(2x+5)sqrt(5x+6) }}}
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Notice the denominator cancels on the left.  On the right we have:
{{{ 12 = sqrt((2x+5)(5x+6)) }}}
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Now, we square both sides:
{{{ 144 = (2x+5)(5x+6) }}}
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Using FOIL, we expand the right side:
{{{ 144 = 10x^2 + 25x + 12x + 30 }}}
{{{ 144 = 10x^2 + 37x + 30 }}}
{{{ 0 = 10x^2 + 37x - 114 }}}
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Since, we can't factor, we must use the quadratic equation.  Doing so, will produce two solutions:
x = {2, -5.7}
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Reference: here is the quadratic solution
*[invoke quadratic "x", 10, 37, -114 ]