Question #296de

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Answer 1 · 2018-01-08T21:08:07

$x~~-2.31,-0.19$

First we square both sides:
$(sqrt(4)/sqrt(4x+9))^2=(sqrt(8x+2))^2$

$(sqrt(4))^2/(sqrt(4x+9))^2=(sqrt(8x+2))^2$

$4/(4x+9)=8x+2$

Now we can rearrange and make it eqial to 0:
$4=(8x+2)(4x+9)$
$(8x+2)(4x+9)-4=0$

Now expand brackets:

$(8x*4x)+(2*4x)+(8x*9)+(2*9)-4=0$

$32x^2+8x+72x+18-4=0$

$32x^2+80x+14=0$

We can remove out common factors:

$32x^2+80x+14=0$

$16x^2+40x+7=0$

$x=(-b+-sqrt(b^2-4ac))/(2a)$

$x=(-40+-sqrt(40^2-4(16*7)))/32$

$=(-40+-sqrt(1600-4(112)))/32$

$=(-40+-sqrt(1600-448))/32$

$=(-40+-sqrt(1152))/32$

$=(-40+sqrt(1152))/32or(-40-sqrt(1152))/32$

$~~-2.31or-0.19$