How do you solve $\sqrt{5 x + 56} - 6 = 3 x - 12$ $\sqrt { 5x + 56} - 6= 3x - 12$ ?

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Answer 1 · 2017-06-20T20:05:19

$x = - \frac{4}{9}, 5$ $x=-4/9, 5$

$\sqrt{5 x + 56} - 6 = 3 x - 12$ $sqrt(5x+56)−6=3x−12$

The first step is to isolate the radicand.

$\sqrt{5 x + 56} = 3 x - 6$ $sqrt(5x+56)=3x-6$

Next, square both sides of the equation to cancel out the radical.

$\sqrt{{(5 x + 56)}^{2}} = {(3 x - 6)}^{2}$ $sqrt((5x+56)^2)=(3x-6)^2$
$5 x + 56 = 9 x^{2} - 36 x + 36$ $5x+56=9x^2 -36x +36$

Move all the terms to one side so it can be factored.

$0 = 9 x^{2} - 41 x - 20$ $0=9x^2-41x-20$

Foil the side with all the terms.

$0 = (9 x + 4) (x - 5)$ $0=(9x+4)(x-5)$

Set each factor equal to 0.

$0 = 9 x + 4$ $0=9x+4$
$0 = x - 5$ $0=x-5$

Solve each equation for x.

$x = - \frac{4}{9}, 5$ $x=-4/9, 5$

Now you have your answer! :)

How do you solve \sqrt { 5x + 56} - 6= 3x - 12√5x+56−6=3x−12\sqrt { 5x + 56} - 6= 3x - 12?