How do you solve $–4 sqrt(x+2) + 3 = -9$ ?

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Answer 1 · 2016-06-20T03:33:20

$x=7$

First, isolate the term including $x$ using subtraction.

$-4sqrt(x+2)+3 = -9$

$=>-4sqrt(x+2)+3-3 = -9 - 3$

$=> -4sqrt(x+2) = -12$

Next, change the coefficient of $sqrt(x+2)$ to $1$ using division.

$=> (-4sqrt(x+2))/(-4) = (-12)/(-4)$

$=> sqrt(x+2) = 3$

Next, eliminate the square root by squaring each side.

$=>(sqrt(x+2))^2 = 3^2$

$=> x+2 = 9$

Finally, isolate $x$ using subtraction.

$=> x+2-2 = 9-2$

$=>x = 7$

And, as good practice, check your answer:

$-4sqrt(7+2)+3 = -4sqrt(9)+3$

$=-4(3)+3$

$=-12+3$

$=-9$

as desired.

How do you solve –4 sqrt(x+2) + 3 = -9–4 sqrt(x+2) + 3 = -9?